Free Printable Unit 10 Super Quizizz Review

1.

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

2.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

3.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

4.

Use a double-angle or half-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

5.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

6.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

7.

Use the information about the angle θ, 0≤θ<2π to find the exact value of
sin (2θ)
1. sin θ= 3/5 , 0<θ<π/2

a)

24/7

b)

7/25

c)

24/25

d)

1/2

8.

sin2u =

a)

(sinu)(cosu)

b)

2(sinu)(cosu)

c)

(sinu)^2

d)

2(sinu)^2

9.

cos2u =

a)

2(sinu)(cosu)

b)

(cosu)^2 - (sinu)^2

c)

2(cosu)^2 - 2

d)

(sinu)^2 - (cosu)^2

10.

If cosx = - 4/5, find secx.

a)

-5/4

b)

-3/5

c)

5/3

d)

√3/2

11.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

12.

Using the second identity, find Cos(50)

a)

sin²(25) - cos²(25)

b)

cos²(50) - sin²(50)

c)

cos²(25) - sin²(25)

d)

sin²(50) - cos²(50)

13.

Using the first identity, find Sin(180)

a)

2sin(90)cos(90)

b)

2sin(180)cos(180)

c)

sin(90)cos(90)

d)

sin(180)cos(180)

14.

Using the third identity, find Cos(40)

a)

2cos² (40) - 1

b)

2cos² (20) - 1

c)

2cos² (20) + 1

d)

2cos² (40) + 1

15.

Using the fourth identity, find Cos(120)

a)

1-2sin²(120)

b)

1+2sin²(120)

c)

1+2sin²(60)

d)

1-2sin²(60)

16.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

17.

Use the Half-angle formulas to find the exact value of each expression
sin 22.5º

a)

√(2 + √3)/2

b)

√(2 - √2)/2

c)

√(2 + √2)/2

d)

√(2 - √3)/2

18.

Which identity represents a double-angle identity for sin 2θ?

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

19.

Use Sum or Difference Identities to find the exact value of each expression.

cos(75°)

a)

1/4

b)

c)

d)

20.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$\tan\theta=-\sqrt{3}$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

21.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$6\sin\theta=3$

a)

$60\degree$

b)

$300\degree$

c)

$30\degree$

d)

$150\degree$

22.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$4\cos\theta=-2$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

23.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$-1+\sin\theta=-1$

a)

$0\degree$

b)

$90\degree$

c)

$180\degree$

d)

$270\degree$

e)

$360\degree$

24.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$5+\tan\theta=4$

a)

$45\degree$

b)

$135\degree$

c)

$225\degree$

d)

$315\degree$

25.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$-15+4\cos\theta=-15-2\sqrt{2}$

a)

$45\degree$

b)

$135\degree$

c)

$225\degree$

d)

$315\degree$

26.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$1-2\sin\theta=-1$

a)

$0\degree$

b)

$90\degree$

c)

$180\degree$

d)

$270\degree$

e)

$360\degree$

27.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$-12-3\tan\theta=-12+\sqrt{3}$

a)

$30\degree$

b)

$150\degree$

c)

$210\degree$

d)

$330\degree$

28.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$2\sin\theta\cos\theta-\sqrt{2}\cos\theta=0$

a)

$45\degree$

b)

$90\degree$

c)

$135\degree$

d)

$270\degree$

e)

$315\degree$

29.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$\sin\theta\tan\theta-\sqrt{3}\sin\theta=0$

a)

$0\degree$

b)

$60\degree$

c)

$180\degree$

d)

$240\degree$

e)

$360\degree$

30.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

31.

TRUE or FALSE:
There is NO SOLUTION to sinθ = -1.

a)

TRUE

b)

FALSE

32.

Solve sinθ = ½ on θ∈[0, 2π)

a)

θ = π / 6, 7π / 6

b)

θ = π / 6, 5π / 6

c)

θ = 5π / 6, 7π / 6

d)

θ = 7π / 6, 11π / 6

33.

Solve sinθ = -1 on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

34.

Solve
cos θ = -1
on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

35.

Which of these is NOT
a solution to
tan θ = 0 ?

a)

θ = 0

b)

θ = π /2

c)

θ = π

d)

θ = 2π

36.

Solve
cos²θ = ½
on θ∈[0, 2π)

a)

θ = π /4, 7π /4

b)

θ = π /4, 3π /4

c)

θ = 3π /4, 5π /4

d)

θ = π /4, 3π /4, 5π /4, 7π /4

37.

Solve
cosθ = - √(3)/2
on θ∈[0, 2π)

a)

θ = π /3, 2π /3

b)

θ = 2π /3, 4π /3

c)

θ = π /6, 5π /6

d)

θ = 5π /6, 7π /6

38.

a)

A

b)

B

c)

C

d)

D

39.

Solve on the Interval [0,2π)
tan(x)+1=2

a)

0 and π

b)

3π/4 and 7π/4

c)

π/4 and 5π/4

d)

3π/4 and 5π/4

40.

a)

No solution

b)

π/3 +2πn, 5π/3 +2πn

c)

π/6 +2πn, 11π/6 +2πn

d)

2π/3 +2πn, 4π/3 +2πn

41.

2 sinθ+3=2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

42.

Solve on the domain [0,2π)
cos x + 1 = 0

a)

0

b)

No solution

c)

π

d)

3π/2

43.

Solve on the domain [0, 2π)
1/2sec x - 1 = 0

a)

π/6, 5π/6

b)

π/3, 5π/3

c)

2π/3, 4π/3

d)

7π/6, 11π/6

44.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

45.

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

46.

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

a)

π

b)

3π/2

c)

π/6, 5π/6, 3π/2

d)

No solution

47.

Solve on the domain [0, 2π)
cos x + 2 = 3 cos x

a)

0, 2π/3, 4π/3

b)

π

c)

0

d)

No solution

48.

Solve on the domain [0,2π)
1/4sin x + 1= 0

a)

0

b)

7π/4

c)

5π/4

d)

No solution

49.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

50.

Solve: 4sinθ + 1 = 3

State all solutions in the interval [0, 2π)

a)

π/ 6, 7π/6

b)

π/6, 5π/ 6

c)

5π/6, 7π/6

d)

7π/6, 11π/6

51.

Solve: 2cscθ + 2 = 0

State all solutions in the interval [0, 2π)

a)

π/2, 3π/2

b)

π/2

c)

3π /2

d)

π

52.

Solve: $2\sqrt{3}\sec\theta\ +\ 4\ =\ 0$
State all solutions in the interval [0, 2π)

a)

π /3, 2π/3

b)

2π /3, 4π/3

c)

π /6, 5π/6

d)

5π /6, 7π/6

53.

Solve: 2cosx - 4 = 0

State all solutions in the interval [0, 2π)

a)

No solution

b)

π/3, 5π/3

c)

π/6, 11π/6

d)

2π/3, 4π/3

54.

Solve: 4sin²x = 3

State all solutions in the interval [0, 2π)

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

55.

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

a)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

56.

Solve equation for $0\le\theta<2\pi$ .
$2=-4-3\csc\theta$

a)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

b)

$\theta=\frac{\pi}{3}$

c)

$\theta=\frac{7\pi}{6},\frac{11\pi}{6}$

d)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}$

57.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\pi$

58.

Solve equation for $0\le\theta<2\pi$ .
$3\tan^2\theta\ -1\ =\ 0$

a)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

59.

Solve equation for $0\le\theta<2\pi$ .
$6\tan\theta\ +\ 6\sqrt{3}\ =\ 0$

a)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

b)

$\theta=\frac{5\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{2\pi}{3},\frac{5\pi}{3}$

60.

Solve equation for $0\le\theta<2\pi$ .
$0=2\sin^2\theta\ +\ \sqrt{3}\sin\theta$

a)

$\theta=0,\frac{2\pi}{3},\pi,\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

c)

$\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$

d)

$\theta=0,\pi,\frac{5\pi}{3}$

61.

$Solve\ \ 2\sin^2x\ +\ \sin x\ -\ 1\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{6},\ \frac{\pi}{2},\ \frac{5\pi}{6}$

b)

$\frac{\pi}{2},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

c)

$\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{3\pi}{2}$

d)

$\frac{7\pi}{6},\ \frac{3\pi}{2},\ \frac{11\pi}{6}$

62.

$Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{4},\ \frac{\pi}{2},\ \frac{5\pi}{4},\ \frac{3\pi}{2}$

b)

$0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$

c)

$\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$

d)

$0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$

63.

Solve the equation. Restrict your answer to [0,2π).

$-2\sqrt{2}=4\sin3\theta$

a)

$\left\{\frac{\pi}{24},\frac{13\pi}{24},\frac{7\pi}{12},\frac{25\pi}{24},\frac{29\pi}{24},\frac{5\pi}{4},\frac{7\pi}{4}\right\}$

b)

$\left\{\frac{7\pi}{12},\frac{25\pi}{24},\frac{13\pi}{12},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

c)

$\left\{\frac{25\pi}{24},\frac{41\pi}{24},\frac{7\pi}{4}\right\}$

d)

$\left\{\frac{5\pi}{12},\frac{7\pi}{12},\frac{13\pi}{12},\frac{5\pi}{4},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

64.

State the solutions in the interval $\left[0,\ 2\pi\right)$
$3\tan3x\ -\ \sqrt{3}\ =\ 0$

a)

$\frac{\pi}{18},\ \frac{7\pi}{18},\ \frac{13\pi}{18},\ \frac{19\pi}{18},\ \frac{25\pi}{18},\ \frac{31\pi}{18}$

b)

$\frac{\pi}{18},\ \frac{13\pi}{18},\ \frac{25\pi}{18}$

c)

$\frac{7\pi}{18},\ \frac{19\pi}{18},\ \frac{31\pi}{18}$

d)

$\frac{\pi}{9},\ \frac{4\pi}{9},\ \frac{7\pi}{9},\ \frac{10\pi}{9},\ \frac{13\pi}{9},\ \frac{16\pi}{9}$

65.

Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree

a)

$x\ =\ 60\degree,\ 120\degree$

b)

$x\ =\ 60\degree,\ 300\degree$

c)

$x\ =\ 30\degree,\ 150\degree$

d)

$x\ =\ 30\degree,\ 330\degree$

66.

$Solve\ \ \tan\ x\ +\ \sqrt{3}\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360\degree$

a)

$30\degree,\ 210\degree$

b)

$150\degree,\ 330\degree$

c)

$60\degree,\ 240\degree$

d)

$120\degree,\ 300\degree$

67.

$Solve\ \ 2\sin^2x\ -\ 1\ =\ 1\ for\ 0\ \le\ x\ <\ 2\pi$

a)

$0,\ \pi$

b)

$\frac{\pi}{2},\ \frac{3\pi}{2}$

c)

$0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2}$

d)

No solution

68.

$Solve\ 3\cot x\ +\ 5\ =\ 8\ \ for\ \ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{2},\ \frac{3\pi}{2}$

b)

$0,\ \pi$

c)

$\frac{3\pi}{4},\ \frac{7\pi}{4}$

d)

$\frac{\pi}{4},\ \frac{5\pi}{4}$

69.

$Solve\ \ \ 3\sec^2x\ =\ 4\ \ for\ \ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

b)

$\frac{\pi}{3},\ \frac{2\pi}{3},\ \frac{4\pi}{3},\ \frac{5\pi}{3}$

c)

$\frac{\pi}{4},\ \frac{3\pi}{4},\ \frac{5\pi}{4},\ \frac{7\pi}{4}$

d)

$0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2}$

70.

$Solve\ \ 6\ +\ 4\csc x\ =\ 14\ \ for\ \ 0\le\ x\ <\ 2\pi$

a)

$\frac{\pi}{3},\ \frac{2\pi}{3}$

b)

$\frac{4\pi}{3},\ \frac{5\pi}{3}$

c)

$\frac{7\pi}{6},\ \frac{11\pi}{6}$

d)

$\frac{\pi}{6},\ \frac{5\pi}{6}$

71.

$Solve\ \ 3\tan x\ +\ 2\ =\ 2\ \ for\ \ 0\ \le\ x\ <\ 2\pi$

a)

No solution

b)

$0,\ \pi$

c)

$\frac{\pi}{2},\ \frac{3\pi}{2}$

d)

$\frac{\pi}{4},\ \frac{5\pi}{4}$

72.

$Solve\ \ 3\sin x\ +\ 4\ =\ 6\ \ for\ \ 0\ \le\ x\ <\ 360\degree.$ Round to the nearest 10th of a degree.

a)

$41.8\degree,\ 138.2\degree$

b)

$48.1\degree,\ 131.9\degree$

c)

$221.8\degree,\ 318.2\degree$

d)

$228.1\degree,\ 311.9\degree$

73.

$Solve\ \ 2\sin^2x\ +\ \sin x\ -\ 1\ =\ 0\ \ for\ 0\ \le\ x\ <\ 360$

a)

$30\degree,\ 90\degree,\ 150\degree$

b)

$90\degree,\ 210\degree,\ 330\degree$

c)

$30\degree,\ 150\degree,\ 270\degree$

d)

$210\degree,\ 270\degree,\ 330\degree$

74.

$Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{4},\ \frac{\pi}{2},\ \frac{5\pi}{4},\ \frac{3\pi}{2}$

b)

$0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$

c)

$\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$

d)

$0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$

75.

Solve the trigonometric equation sin 2x = 2 sin x for over the interval . [0, π/2]

a)

0 degrees

b)

30 degrees

c)

60 degrees

d)

90 degrees

76.

Solve the trigonometric equation sin²2θ = 2sin²θ for θ in the interval [0, π/2)

a)

0 and π/4

b)

0 and π/6

c)

0 and π/2

d)

π/3 and π/6

77.

Solve the following equation for 0 ≤ x ≤ 2π. sin 2x + sin x = 0

a)

x = 0, 2π/3, π, 4π/3

b)

x = 0, -2π/3, π, 4π/3

c)

x = 0, 2π/3, -π, 4π/3

d)

x = 0, 2π/3, π, -4π/3

78.

Solve the trigonometric equation sin 2x/(1 + cos 2x) = 1 for θ in the interval [0, π].

a)

π/4

b)

π/2

c)

π/3

d)

π/6

79.

Solve the following equation for 0 ≤ x ≤ 2π. cos 2x - 1 = sin²x

a)

x = 0, π

b)

x = -1, π

c)

x = 2, π

d)

x = 0, -π

80.

Solve the following equation for 0 ≤ x ≤ 2π. sin 2x cos x = sin x.

a)

x = 0, π/4, 3π/4, π, 5π/4, 7π/4

b)

x = 0, -π/4, 3π/4, π, 5π/4, 7π/4

c)

x = 0, π/4, -3π/4, -π, 5π/4, 7π/4

d)

x = 0, π/4, -3π/4, π, -5π/4, 7π/4

81.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

82.

Solve the following equation for 0 ≤ x ≤ 2π. tan 2x - tan x = 0

a)

x = 0, π

b)

x = π/2, π/4

c)

x = π/6, π/2

d)

x = π/2, π/3

83.

Solve the following equation for 0 ≤ x ≤ 2π. cos²x - cos 2x = 0

a)

x = 0, π

b)

x = 0, -π

c)

x = -1, π

d)

x = 2, π

84.

Solve the following equation for 0 ≤ x ≤ 2π. cos 2x = cos x

a)

x = 0, 2π/3, 4π/3

b)

x = 0, -2π/3, -4π/3

c)

x = 0, -2π/3, 4π/3

d)

x = 0, π/, 2π

85.

Simplify cos x tan x.

a)

csc x

b)

sin x

c)

1

d)

cos x

86.

Simplify cos x + cos x tan² x

a)

sec x

b)

1 + tan x

c)

csc x

d)

tan x

87.

If csc x = 2, find sin x .

a)

$\sqrt{2}$

b)

$\frac{\sqrt{3}}{2}$

c)

1/2

d)

2

88.

Solve $\sin^2x-\sin x+1=\cos^2x\ for\ 0\le x<2\pi$ .

a)

$0,\ \frac{\pi}{6},\ \frac{5\pi}{6}$

b)

$0,\ \frac{3\pi}{4},\ \frac{5\pi}{6},\ \pi$

c)

$0,\ \frac{\pi}{6},\ \frac{5\pi}{6},\ \pi$

d)

$0,\ \frac{\pi}{6},\ \frac{\pi}{3},\ \pi$

89.

Solve $4\sin^2x+3=4$ for principal values of x. Express solutions in radians.

a)

$\frac{\pi}{6},\ \frac{5\pi}{6}$

b)

$\frac{\pi}{3},\ \frac{2\pi}{3}$

c)

$-\frac{\pi}{6},\ \frac{\pi}{6}$

d)

$-\frac{\pi}{3},\ \frac{\pi}{3}$

90.

Solve $\sqrt{2}\cos x-1\ =\ 0$ for all real values of x.

a)

$\frac{\pi}{4}+2\pi k,\ \frac{7\pi}{4}+2\pi k$

b)

$\frac{\pi}{6}+2\pi k,\ \frac{5\pi}{6}+2\pi k$

c)

$\frac{\pi}{4}+\pi k$

d)

$\frac{3\pi}{4}+2\pi k,\ \frac{5\pi}{4}+2\pi k$

91.

Use the sum or difference identity for sine to find the exact value of sin $375\degree$ .

a)

$\frac{\sqrt{3}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

92.

If sin x = 1/3 and x has its terminal side in the first quadrant, find the exact value of sin 2x.

a)

$\frac{2\sqrt{2}}{3}$

b)

$\frac{4\sqrt{2}}{3}$

c)

$\frac{4\sqrt{2}}{9}$

d)

$\frac{2}{3}$

93.

Use a half-angle identity to find the exact value of $\sin\ 67.5\degree$ .

a)

$\frac{\sqrt{2+\sqrt{2}}}{2}$

b)

$\frac{\sqrt{1+\sqrt{2}}}{2}$

c)

$\frac{\sqrt{2-\sqrt{2}}}{2}$

d)

$\frac{\sqrt{1-\sqrt{2}}}{2}$

94.

Complete the identity $\frac{\sin x\cos x}{1-\cos^2x}=_{ }$ ________ .

a)

cos x

b)

tan x

c)

cot x

d)

sin x

95.

If f(x) = sin(x) and g(x) = cos(x), then f(2x) =

a)

2f(x)

b)

f(2)f(x)

c)

2f(x)g(x)

d)

f(x)g(x)

96.

$\sin\left(22.5\degree\right)=$

a)

$\frac{\sqrt[]{2}}{4}$

b)

$\frac{\sqrt[]{2-\sqrt[]{2}}}{2}$

c)

$\frac{\left(\sqrt[]{6}-\sqrt[]{2}\right)}{4}$

d)

$\sqrt[]{\frac{\left(2-\sqrt[]{2}\right)}{2}}$

97.

How many numbers between $0\ and\ 2\pi$ satisfy the equation $\sin\left(2x\right)=\cos\left(x\right)$ ?

a)

four

b)

two

c)

one

d)

none

98.

Write the expression $2\sin\left(2x\right)\cos\left(2x\right)$ as a single term.

a)

$\cos\left(4x\right)$

b)

$\sin\left(4x\right)$

c)

$\sin\left(2x\right)$

d)

$\sin\left(4x^2\right)$

99.

a)

A

b)

B

c)

C

d)

D

100.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

101.

a)

A

b)

B

c)

C

d)

D

102.

Solve for ALL answers such that

0\le x<2\pi

:

0=\sin2x

a)

$x=0,\frac{\pi}{2},\pi,\frac{3\pi}{2}$

b)

$x=0,\pi$

c)

$No\ Solutions$

d)

$x=0,\pi,2\pi,3\pi$

103.

Solve for ALL answers such that

0\le x<2\pi

:

\frac{1}{2}=\sin3x

a)

$x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18},\frac{25\pi}{18},\frac{29\pi}{18}$

b)

$x=\frac{\pi}{18},\frac{5\pi}{18},\frac{13\pi}{18},\frac{17\pi}{18}$

c)

$x=\frac{\pi}{6},\frac{5\pi}{6},\frac{13\pi}{6},\frac{17\pi}{6},\frac{25\pi}{6},\frac{29\pi}{6}$

d)

$x=\frac{\pi}{6},\frac{5\pi}{6}$

104.

Solve for ALL answers such that

0\le x<2\pi

:

\cos2x=\frac{\sqrt{2}}{2}

a)

$x=\frac{\pi}{8},\frac{7\pi}{8},\frac{9\pi}{8},\frac{15\pi}{8}$

b)

$x=\frac{\pi}{4},\frac{7\pi}{4},\frac{9\pi}{4},\frac{15\pi}{4}$

c)

$x=\frac{\pi}{4},\frac{7\pi}{4}$

d)

$No\ Solution$

105.

Solve for ALL answers such that

0\le x<2\pi

:

\csc3x=-\frac{2\sqrt{3}}{3}

a)

$x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9}$

b)

$x=\frac{4\pi}{9},\frac{5\pi}{9},\frac{10\pi}{9},\frac{11\pi}{9},\frac{16\pi}{9},\frac{17\pi}{9}$

c)

$x=\frac{4\pi}{3},\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3},\frac{16\pi}{3},\frac{17\pi}{3}$

d)

$No\ Solutions$

106.

Solve for ALL answers such that

0\le x<2\pi

:

-\frac{\sqrt{3}}{2}=\cos3x

a)

$x=\frac{5\pi}{18},\frac{7\pi}{18},\frac{17\pi}{18},\frac{19\pi}{18},\frac{29\pi}{18},\frac{31\pi}{18}$

b)

$x=\frac{5\pi}{6},\frac{7\pi}{6},\frac{17\pi}{6},\frac{19\pi}{6},\frac{29\pi}{6},\frac{31\pi}{6}$

c)

$No\ Solutions$

d)

$x=\frac{5\pi}{6},\frac{7\pi}{6}$

107.

Solve for ALL answers such that

0\le x<2\pi

:

-\frac{\sqrt{3}}{2}=\sin x

a)

$x=\frac{4\pi}{3},\frac{5\pi}{3}$

b)

$x=\frac{\pi}{3},\frac{2\pi}{3}$

c)

$No\ Solutions$

d)

$x=\frac{\pi}{3},\frac{5\pi}{3}$

108.

Solve for ALL answers such that

0\le x<2\pi

:

\frac{\sqrt{3}}{2}=\cos2x

a)

$x=\frac{\pi}{12},\frac{11\pi}{12},\frac{13\pi}{12},\frac{23\pi}{12}$

b)

$x=\frac{\pi}{6},\frac{11\pi}{6},\frac{13\pi}{6},\frac{23\pi}{6}$

c)

$No\ Solutions$

d)

$x=\frac{\pi}{6},\frac{11\pi}{6}$

109.

Solve for ALL answers such that

0\le x<2\pi

:

\tan3x=1

a)

$x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4}$

b)

$x=\frac{\pi}{4},\frac{5\pi}{4},\frac{9\pi}{4},\frac{13\pi}{4},\frac{17\pi}{4},\frac{21\pi}{4}$

c)

$No\ Solutions$

d)

$x=\frac{\pi}{4},\frac{5\pi}{4}$

110.

Solve: 4sinθ + 1 = 3

State all solutions in the interval [0, 2π)

a)

π/ 6, 7π/6

b)

π/6, 5π/ 6

c)

5π/6, 7π/6

d)

7π/6, 11π/6

111.

Solve: 2cscθ + 2 = 0

State all solutions in the interval [0, 2π)

a)

π/2, 3π/2

b)

π/2

c)

3π /2

d)

π

112.

Solve: $2\sqrt{3}\sec\theta\ +\ 4\ =\ 0$
State all solutions in the interval [0, 2π)

a)

π /3, 2π/3

b)

2π /3, 4π/3

c)

π /6, 5π/6

d)

5π /6, 7π/6

113.

Solve: 2cosx - 4 = 0

State all solutions in the interval [0, 2π)

a)

No solution

b)

π/3, 5π/3

c)

π/6, 11π/6

d)

2π/3, 4π/3

114.

Solve: 4sin²x = 3

State all solutions in the interval [0, 2π)

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

115.

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

a)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

116.

Solve equation for $0\le\theta<2\pi$ .
$2=-4-3\csc\theta$

a)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

b)

$\theta=\frac{\pi}{3}$

c)

$\theta=\frac{7\pi}{6},\frac{11\pi}{6}$

d)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}$

117.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\pi$

118.

Solve equation for $0\le\theta<2\pi$ .
$3\tan^2\theta\ -1\ =\ 0$

a)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

119.

Solve equation for $0\le\theta<2\pi$ .
$6\tan\theta\ +\ 6\sqrt{3}\ =\ 0$

a)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

b)

$\theta=\frac{5\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{2\pi}{3},\frac{5\pi}{3}$

120.

Solve equation for $0\le\theta<2\pi$ .
$0=2\sin^2\theta\ +\ \sqrt{3}\sin\theta$

a)

$\theta=0,\frac{2\pi}{3},\pi,\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

c)

$\theta=0,\pi,\frac{4\pi}{3},\frac{5\pi}{3}$

d)

$\theta=0,\pi,\frac{5\pi}{3}$

121.

$Solve\ \ 2\sin^2x\ +\ \sin x\ -\ 1\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{6},\ \frac{\pi}{2},\ \frac{5\pi}{6}$

b)

$\frac{\pi}{2},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

c)

$\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{3\pi}{2}$

d)

$\frac{7\pi}{6},\ \frac{3\pi}{2},\ \frac{11\pi}{6}$

122.

$Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{4},\ \frac{\pi}{2},\ \frac{5\pi}{4},\ \frac{3\pi}{2}$

b)

$0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$

c)

$\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$

d)

$0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$

123.

Solve the equation. Restrict your answer to [0,2π).

$-2\sqrt{2}=4\sin3\theta$

a)

$\left\{\frac{\pi}{24},\frac{13\pi}{24},\frac{7\pi}{12},\frac{25\pi}{24},\frac{29\pi}{24},\frac{5\pi}{4},\frac{7\pi}{4}\right\}$

b)

$\left\{\frac{7\pi}{12},\frac{25\pi}{24},\frac{13\pi}{12},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

c)

$\left\{\frac{25\pi}{24},\frac{41\pi}{24},\frac{7\pi}{4}\right\}$

d)

$\left\{\frac{5\pi}{12},\frac{7\pi}{12},\frac{13\pi}{12},\frac{5\pi}{4},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

124.

State the solutions in the interval $\left[0,\ 2\pi\right)$
$3\tan3x\ -\ \sqrt{3}\ =\ 0$

a)

$\frac{\pi}{18},\ \frac{7\pi}{18},\ \frac{13\pi}{18},\ \frac{19\pi}{18},\ \frac{25\pi}{18},\ \frac{31\pi}{18}$

b)

$\frac{\pi}{18},\ \frac{13\pi}{18},\ \frac{25\pi}{18}$

c)

$\frac{7\pi}{18},\ \frac{19\pi}{18},\ \frac{31\pi}{18}$

d)

$\frac{\pi}{9},\ \frac{4\pi}{9},\ \frac{7\pi}{9},\ \frac{10\pi}{9},\ \frac{13\pi}{9},\ \frac{16\pi}{9}$

125.

$2\sin\left(10\right)\cos\left(10\right)=$

a)

$\sin\left(5\right)\cos\left(5\right)$

b)

$\sin\left(20\right)\cos\left(20\right)$

c)

$\cos\left(20\right)$

d)

$\sin\left(20\right)$

126.

$\cos^2\left(10\right)-\sin^2\left(10\right)=$

a)

$\cos\left(20\right)$

b)

$\sin\left(20\right)$

c)

1

d)

$\cos\left(100\right)-\sin\left(100\right)$

127.

$\sin\left(40\right)\cos\left(40\right)=$

a)

$\frac{1}{2}\sin\left(80\right)$

b)

$\frac{1}{2}\cos\left(80\right)$

c)

$\sin\left(80\right)$

d)

$\cos\left(80\right)$

128.

$\frac{2\tan\left(50\right)}{1-\tan^2\left(50\right)}=$

a)

$\frac{1}{2}\tan\left(100\right)$

b)

$\frac{1}{2}\tan\left(50\right)$

c)

$\tan\left(100\right)$

d)

$\tan\left(50\right)$

129.

$1-2\sin^2x=$

a)

$\sin\left(2x\right)$

b)

$\cos\left(2x\right)$

c)

$\tan\left(2x\right)$

130.

$2\sin\left(3x\right)\cos\left(3x\right)=$

a)

$\sin\left(6x\right)$

b)

$\sin\left(6x\right)\cos\left(6x\right)$

c)

$\cos\left(6x\right)$

d)

$\sin\left(3x\right)$

131.

$2\cos^2x-2\sin^2x=$

a)

$2\cos\left(2x\right)$

b)

$\cos\left(4x\right)$

c)

$2\sin\left(2x\right)$

d)

$\sin\left(4x\right)$

132.

$\frac{2\tan\left(40\right)}{1-\tan^2\left(40\right)}=$

a)

$\frac{\tan\left(80\right)}{1-\tan\left(1600\right)}$

b)

$\tan\left(40\right)$

c)

$\tan\left(80\right)$

d)

$2\tan\left(40\right)$

133.

$2\cos^2\left(25\right)-1=$

a)

$\cos\left(1250\right)-1$

b)

$\cos\left(50\right)$

c)

$\sin\left(50\right)$

d)

$\cos\left(25\right)$

134.

$10\sin x\cos x=$

a)

$\sin\left(10x\right)$

b)

$\sin\left(5x\right)$

c)

$5\sin\left(2x\right)$

d)

$5\cos\left(2x\right)$

135.

$\sin\left(2x\right)\cos\left(2x\right)=$

a)

$\sin\left(2x\right)$

b)

$2\sin\left(4x\right)$

c)

$\sin\left(4x\right)$

d)

$\frac{1}{2}\sin\left(4x\right)$

136.

$4-8\sin^2x=$

a)

$1-\sin^2x$

b)

$4\cos\left(2x\right)$

c)

$4\sin\left(2x\right)$

d)

$\cos\left(8x\right)$

137.

$\cos^2\left(5x\right)-\sin^2\left(5x\right)=$

a)

$\cos\left(10x\right)$

b)

$\sin\left(10x\right)$

c)

$\cos\left(5x\right)$

d)

$\sin\left(5x\right)$

138.

$1-2\sin^2\left(40\right)=$

a)

$1-\sin^2\left(80\right)$

b)

$\cos\left(80\right)$

c)

$\sin\left(80\right)$

d)

$\cos\left(40\right)$

139.

$\frac{6\tan\left(5\right)}{1-\tan^2\left(5\right)}=$

a)

$\tan\left(5\right)$

b)

$\tan\left(10\right)$

c)

$3\tan\left(10\right)$

d)

$3\tan\left(5\right)$

140.

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

141.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

142.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

143.

Use a double-angle or half-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

144.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

145.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

146.

Use the information about the angle θ, 0≤θ<2π to find the exact value of
sin (2θ)
1. sin θ= 3/5 , 0<θ<π/2

a)

24/7

b)

7/25

c)

24/25

d)

1/2

147.

sin2u =

a)

(sinu)(cosu)

b)

2(sinu)(cosu)

c)

(sinu)^2

d)

2(sinu)^2

148.

cos2u =

a)

2(sinu)(cosu)

b)

(cosu)^2 - (sinu)^2

c)

2(cosu)^2 - 2

d)

(sinu)^2 - (cosu)^2

149.

If cosx = - 4/5, find secx.

a)

-5/4

b)

-3/5

c)

5/3

d)

√3/2

150.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

151.

Using the second identity, find Cos(50)

a)

sin²(25) - cos²(25)

b)

cos²(50) - sin²(50)

c)

cos²(25) - sin²(25)

d)

sin²(50) - cos²(50)

152.

Using the first identity, find Sin(180)

a)

2sin(90)cos(90)

b)

2sin(180)cos(180)

c)

sin(90)cos(90)

d)

sin(180)cos(180)

153.

Using the third identity, find Cos(40)

a)

2cos² (40) - 1

b)

2cos² (20) - 1

c)

2cos² (20) + 1

d)

2cos² (40) + 1

154.

Using the fourth identity, find Cos(120)

a)

1-2sin²(120)

b)

1+2sin²(120)

c)

1+2sin²(60)

d)

1-2sin²(60)

155.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

156.

Use the Half-angle formulas to find the exact value of each expression
sin 22.5º

a)

√(2 + √3)/2

b)

√(2 - √2)/2

c)

√(2 + √2)/2

d)

√(2 - √3)/2

157.

Which identity represents a double-angle identity for sin 2θ?

a)

2sinθcosθ

b)

cos²θ - sin²θ

c)

1 - 2sin²θ

d)

2cos²θ - 1

158.

Use Sum or Difference Identities to find the exact value of each expression.

cos(75°)

a)

1/4

b)

c)

d)

Unit 10 Super Quizizz Review

Total questions: 158

Worksheet time: 7hrs 58mins

Similar Resources on Wayground