Free Printable Unit 3 Review Introduction to Trig and Trig Graphing

1.

How many degrees does circle have?

a)

360 degrees

b)

2pi

c)

180 degrees

d)

pi

2.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

3.

When the rotation from initial to terminal side is counterclockwise this describes.

a)

Positive Angle

b)

Negative Angle

4.

Which quadrant is -5π/6 in?

a)

I

b)

II

c)

III

d)

IV

5.

Which quadrant is 2π/3 in?

a)

I

b)

II

c)

III

d)

IV

6.

In what quadrant is 285°

a)

I

b)

II

c)

III

d)

IV

7.

What is the co-terminal angle of 210⁰ ?

a)

-30⁰

b)

-150⁰

c)

-40⁰

d)

150⁰

8.

What is the co-terminal angle of -80⁰ ?

a)

-10⁰

b)

-280⁰

c)

10⁰

d)

280⁰

9.

What is 5π/6 radians in degrees?

a)

180

b)

150

c)

360

d)

120

10.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

11.

What is 45 degrees in radians?

a)

π/2

b)

π/6

c)

π/4

d)

3π/4

12.

What is 60 degrees in radians?

a)

2π/3

b)

π/3

c)

4π/3

d)

π/6

13.

Find an angle coterminal with an angle which measures 11π ∕ 3.

a)

17 π / 3

b)

4π ∕ 3

c)

π ∕ 3

d)

8π ∕ 3

14.

In a circle with a diameter of 24 cm, a central angle of $\frac{4\pi}{3}$ radians intercepts an arc. The length of the arc, in terms of $\pi$ , is

a)

$16\pi$

b)

$4\pi$

c)

$3\pi$

d)

$32\pi$

15.

Find the length of the arc. (Note that the angle measure is in degrees).

a)

$\frac{17\pi}{2}mi$

b)

$17\pi\ mi$

c)

$\frac{17\pi}{4}mi$

d)

$\frac{51\pi}{2}mi$

16.

Which one is the easy trick to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

17.

Find the ratio for sinA. (Reduce the fraction)

a)

36/27

b)

4/5

c)

36/45

d)

3/5

18.

Solve for x. Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

23.4

19.

Solve for x. Round to the nearest tenth.

a)

9.8

b)

0.1

c)

0.038

d)

9.9

20.

Which trig function would help you solve for the missing angle?

a)

sine

b)

cosine

c)

tangent

d)

pythagorean theorem

21.

Solve for the missing distance

a)

18.9 meters

b)

19.5 meters

c)

47.2 meters

d)

27.5 meters

22.

Solve for the missing angle

a)

50.5 degrees

b)

12.7 degrees

c)

36.9 degrees

d)

72.2 degrees

23.

What is the secant of the given angle?

a)

$\frac{\sqrt{170}}{11}$

b)

$\frac{11\sqrt{170}}{170}$

c)

$\frac{7\sqrt{170}}{170}$

d)

$\frac{\sqrt{170}}{7}$

24.

What is the cotangent of the given angle?

a)

$\frac{7\sqrt{170}}{170}$

b)

$\frac{11\sqrt{170}}{170}$

c)

$\frac{11}{7}$

d)

$\frac{7}{11}$

25.

Write all six trig ratios.

a)

$\sin\theta=\frac{24}{25}\ \cos\theta=\frac{7}{25}\ \tan\theta=\frac{24}{7}\$ $\csc\theta=\frac{25}{24}\ \sec\theta=\frac{25}{7}\ \cot\theta=\frac{7}{24}$

b)

$\sin\theta=\frac{7}{25}\ \cos\theta=\frac{24}{25}\ \tan\theta=\frac{7}{24}$ $\csc\theta=\frac{25}{7}\ \sec\theta=\frac{25}{24}\ \cot\theta=\frac{24}{7}$

26.

Find the remaining trig ratios if $\sin\theta=\frac{2}{3}$

a)

$\cos\theta=\frac{5}{7}\ \tan\theta=\frac{2}{5}$ $\csc\theta=\frac{3}{2}\ \sec\theta=\frac{7}{5}\ \cot\theta=\frac{5}{2}$

b)

$\cos\theta=\frac{2\sqrt{5}}{5}\ \tan\theta=\frac{2}{3}$ $\csc\theta=\frac{3}{2}\ \sec\theta=\frac{\sqrt{5}}{2}\ \cot\theta=\frac{3}{2}$

c)

$\cos\theta=\frac{\sqrt{5}}{2}\ \tan\theta=\frac{2\sqrt{5}}{5}\csc\theta=\frac{3}{2}\ \sec\theta=\frac{2\sqrt{5}}{5}\cot\theta=\frac{5\sqrt{5}}{2}$

d)

$\cos\theta=\frac{\sqrt{5}}{3}\ \tan\theta=\frac{2\sqrt{5}}{5}\csc\theta=\frac{3}{2}\ \sec\theta=\frac{3\sqrt{5}}{5}\cot\theta=\frac{\sqrt{5}}{2}$

27.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

28.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

29.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

30.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

31.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

32.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

33.

tan 7π/4

a)

-1

b)

1

c)

√2/2

d)

undefined

34.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

35.

cot 3π/4

a)

-√2/2

b)

-1

c)

1

d)

√2/2

36.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

37.

cot π/2

a)

undefined

b)

0

c)

1

d)

1/2

38.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

39.

tan (-π)

a)

undefined

b)

0

c)

1

d)

-1

40.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

41.

What are the domain and range of y = arcsin(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain [-1, 1] range [0, π]

c)

domain [-1, 1] range [-π/2, π/2]

d)

domain [0,2π] range [-1, 1]

42.

What are the domain and range of y = arccos(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain [-1, 1] range [0, π]

c)

domain [-1, 1] range [-π/2, π/2]

d)

domain [0, 2π] range [-1, 1]

43.

arctan(-1)

a)

3π/2

b)

π/4

c)

-π/4

d)

3π/4 and 7π/4

44.

arcsin(√3/2)

a)

π/3

b)

-π/3

c)

2π/3

d)

π/3 and 2π/3

45.

arccos(√3/2)

a)

π/6

b)

-π/6

c)

11π/6

d)

π/6 and 11π/6

46.

What are the domain and range of y = arctan(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain (-∞, ∞) range [-π/2, π/2]

c)

domain [-1, 1] range (-π/2, π/2)

d)

domain (-∞, ∞) range (-π/2, π/2)

47.

arccos(-1/2)

a)

π/3

b)

-5π/3

c)

2π/3

d)

2π/3 and 4π/3

48.

Find the reference angle for an angle measuring -300⁰

a)

60⁰

b)

-60⁰

c)

30⁰

d)

45⁰

49.

What is the reference angle for 240 degrees?

a)

60 degrees

b)

30 degrees

c)

45 degrees

d)

210 degrees

50.

What is the reference angle for

\frac{2\pi}{3}

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

$\frac{\pi}{3}$

51.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

52.

what is the amplitude of y=3sin(7x)-2

a)

7

b)

-2

c)

3

d)

6

53.

what is the period of y= -3sinx

a)

π

b)

2π

c)

3π

d)

4π

54.

What is the period?

a)

π/4

b)

π/2

c)

3π/4

d)

π

55.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

56.

What is the period of this graph?

a)

2π

b)

π/2

c)

π/4

d)

π

57.

What is the period of y = 4Cos(2x)?

a)

4π

b)

π

c)

2π

d)

π/2

58.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

59.

What is the amplitude and period of y = 2sin(πx)

a)

2 and 2

b)

π and 2

c)

2 and π

d)

2π and 2

60.

What are the 5-Key Points on the graph of the given function?

y=-3\sin\left(2x\right)+4

a)

$\left(0,0\right)\left(45,3\right)\left(90,4\right)\left(135,1\right)\left(180,4\right)$

b)

$\left(0,4\right)\left(45,1\right)\left(90,4\right)\left(135,7\right)\left(180,4\right)$

c)

$\left(0,0\right)\left(45,-3\right)\left(90,0\right)\left(135,3\right)\left(180,0\right)$

d)

$\left(0,4\right)\left(90,1\right)\left(180,4\right)\left(270,7\right)\left(360,4\right)$

e)

$\left(0,0\right)\left(90,3\right)\left(180,4\right)\left(270,1\right)\left(360,4\right)$

Unit 3 Review Introduction to Trig and Trig Graphing

Total questions: 60

Worksheet time: 1hrs 4mins

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