Free Printable Mr B Trig Practice Unit Circle

1.

What is the value of cos(45)?

a)

√2

b)

√3/2

c)

√2/2

d)

0

e)

1

2.

What is cot(60)?

a)

1/2

b)

√3

c)

1/√2

d)

1/√3

3.

What is the value of sin(60)?

a)

√3/2

b)

1/2

c)

1

d)

0

4.

If cos(x) = 84/85 which of the following could represent tan(x) ?

a)

85/84

b)

84/13

c)

12/85

d)

13/85

e)

13/84

5.

The terminal side of an angle θ in standard position passes through the point (8, -15). What is cos(θ)?

a)

8/17

b)

-8/17

c)

15/17

d)

-15/17

6.

If cos(y) = $\frac{20}{101}$ and y is in the third quadrant, what is sin(y)?

a)

99/101

b)

-20/101

c)

-101/20

d)

-99/101

e)

0

7.

Sin is related to (a) , cos is related to (b) , and tangent is related to (c)

Choose from the below words

Csc

sec

cotangent

8.

What is the reciprocal of tan(x)?

a)

$\frac{1}{\tan\left(x\right)}$

b)

$\frac{\sin\left(x\right)}{\cos\left(x\right)}$

c)

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

d)

$\frac{1}{\cos\left(x\right)}$

9.

If sec(x) =2, what is cos(x)?

a)

-2

b)

1/2

c)

2

d)

-1/2

10.

What is the period of the function y = 3cos(2x) ?

a)

π

b)

π/2

c)

2π

d)

3π

e)

4π

11.

Find the amplitude of y = 5sin(4x) + 2 .

a)

1

b)

4

c)

5

d)

2

12.

What is the range of the function y=3cos⁡(x)?

a)

[-4, 4]

b)

[1, 5]

c)

[0, 3]

d)

[-3, 3]

e)

[-2, 2]

13.

Solve for x: 2 sin(x) = √3, where 0 ≤ x ≤ 2π.

a)

π/3, 2π/3

b)

π/6, 5π/6

c)

π/3, 4π/3

d)

π/4, 3π/4

14.

Which of the following is the equation of a sine function with amplitude 2 and period π?

a)

3sin(x)

b)

sin(4x)

c)

2sin(x/2)

d)

2sin(2x)

15.

Which of the following is true about the function y = -cos(x)?

a)

The graph is shifted π/2 units to the right.

b)

The graph is reflected over the x-axis.

c)

The graph has an amplitude of 0.

d)

The graph is shifted π units to the left.

16.

Convert 60° to radians.

a)

π/6

b)

π/4

c)

π/3

d)

π/2

17.

If sin(x) = 1/2 and x is in the second quadrant, what is x in degrees?

a)

30°

b)

150°

c)

210°

d)

330°

18.

What is the period of y = 3Sin(3x)?

a)

2π/3

b)

π/3

c)

3π

d)

π

19.

$Solvefor\ x:\cos(x)=-1,\ where\ 0\le x\le2\pi.$

a)

π

b)

2π

c)

3π/2

d)

π/2

e)

0

20.

In the unit circle, what are the coordinates of the point at 225°?

a)

(0, 1)

b)

(√2/2, √2/2)

c)

(-√2/2, -√2/2)

d)

(1, 0)

e)

(-1, 1)

21.

$The\ height\ of\ a\ ferris\ wheel\ is\ modeled\ by\ y=20+15\sin(\frac{\pi}{30}t),\ where\ y\ is\ the\ height\ in\ meters\ and\ t\ is\ the\ time\ in\sec onds.\ What\ is\ the\max imum\ height?$

a)

25 meters

b)

30 meters

c)

35 meters

d)

40 meters

22.

If no dilations exist, what is the normal period of a sine or cosine function?

a)

1/2π

b)

2π

c)

π

d)

π/2

23.

Find the amplitude of y=-5cos( $\frac{1}{2x}$ +π)

a)

1

b)

-5

c)

1/2

d)

5

24.

What is the period of y=4cos(5x)

a)

2π/5

b)

5π/2

c)

5

d)

5π

25.

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

a)

7

b)

-2

c)

3

d)

6

26.

a)

1

b)

-1

c)

0

d)

√2/2

27.

a)

-√3/2

b)

-½

c)

-√2/2

d)

-1

28.

Find sin t.

a)

$-\frac{12}{13}$

b)

$-\frac{5}{13}$

c)

$\frac{12}{5}$

d)

$-\frac{13}{12}$

29.

a)

½

b)

√2/2

c)

√3/2

d)

1

30.

In the context of a Unit Circle:

What is the approximate most accurate simplification of 0.866, one-half [either the y or x half; (x, y)] of a coordinate pair in a cartesian Unit Circle representation, which of course does not reach a Unit Square point like, "(1, 1),"

a)

b)

c)

d)

31.

Find $\cos^{-1}$ C

32.

Match the following definitions with the correct word

a)

The ---------- of a number between 0 and 1 is the

acute angle whose cosine is that number.

1.

Arccosine

b)

The --------- of a number between 0 and 1 is the

acute angle whose sine is that number.

2.

Arcsine

c)

The ----------- of a positive number is the acute

angle whose tangent is that number.

3.

Arctangent

33.

What is cos 90°?

a)

½

b)

undefined

c)

1

d)

0

34.

The diagram below shows a unit circle. State the possible values of a and b.

a)

$a=0.9397,\ b=0.3420$

b)

$a=0.9397,\ b=-0.3420$

c)

$a=-0.9397,\ b=0.3420$

d)

$\alpha=-0.9397,\ b=-0.3420$

35.

Using the Unit Circle, find the exact value of this trig function.

a)

b)

c)

d)

e)

The correct answer is not listed

36.

Match the following

a)

$\frac{1}{\sec\left(x\right)}$

1.

cos(x)

b)

$\frac{1}{\cot\left(x\right)}$

2.

tan(x)

c)

$\frac{1}{\csc\left(x\right)}$

3.

sin(x)

37.

Match the following to the trig function used to solve for angle B.

a)

1.

not a right triangle

b)

2.

Inverse Tangent

c)

3.

Inverse Cosine

d)

4.

Inverse Sine

38.

Match the following to find the measure of angle T.

a)

1.

Inverse Tan

b)

2.

Inverse Sin

c)

3.

Inverse Cos

d)

4.

Not a right triangle

39.

$\cos^{-1}\left(\frac{-\sqrt[]{3}}{2}\right)$ = (a)

Choose from the below words

\frac{5\pi}{6}

\frac{-\pi}{6}

$\frac{\pi}{6}$

\frac{2\pi}{3}

\frac{-\pi}{3}

\frac{\pi}{2}

\frac{\pi}{4}

\frac{3\pi}{4}

\frac{-\pi}{4}

\frac{\pi}{3}

40.

$\sin^{-1}\left(-1\right)$ = (a)

Choose from the below words

\frac{-\pi}{6}

$\frac{\pi}{6}$

\frac{-\pi}{3}

\frac{\pi}{2}

\frac{\pi}{4}

\frac{-\pi}{4}

$\frac{-\pi}{2}$

0

\pi

41.

$\sin^{-1}\left(\frac{\sqrt[]{3}}{2}\right)$ = (a)

Choose from the below words

\frac{5\pi}{6}

\frac{-\pi}{6}

$\frac{\pi}{6}$

\frac{2\pi}{3}

\frac{-\pi}{3}

\frac{\pi}{2}

\frac{\pi}{4}

\frac{3\pi}{4}

\frac{-\pi}{4}

\frac{\pi}{3}

42.

$\sin^{-1}\left(\frac{-1}{2}\right)=$ = (a)

Choose from the below words

\frac{-\pi}{6}

$\frac{\pi}{6}$

\frac{-\pi}{3}

\frac{\pi}{2}

\frac{\pi}{4}

\frac{-\pi}{4}

\frac{\pi}{3}

\frac{5\pi}{6}

\frac{2\pi}{3}

\frac{3\pi}{4}

43.

a)

A

b)

B

c)

C

d)

D

44.

a)

b)

c)

d)

45.

a)

b)

c)

d)

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.

What is the vertical shift for y = 4 cos(x) - 2? (a)

Choose from the below words

up 2

left 2

right 2

down 2

48.

what is the amplitude of

y = -3sin (7x) -2

49.

Describe the horizontal shift.

a)

left π / 2

b)

left 2π

c)

right 2π

d)

right π / 2

50.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

51.

a)

y = sin x

b)

y = - sin x

c)

y = cos x

d)

y = - cos x

52.

What is the equation of this graph?

a)

y=cos2x

b)

y=2sin2x

c)

y=2cos2x

d)

y=2sinx

53.

What is the equation of the graph?

a)

y = -2 cos x - 3

b)

y = 3 cos x - 2

c)

y = -7 cos x - 3

d)

y = -3 cos x - 4

54.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

55.

Which function represents the graph?

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = sin ( ⅓ x)

d)

f(x) = sin (3 x)

56.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

57.

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = sin x + 3

d)

f(x) = cos x + 3

Mr B Trig Practice Unit Circle

Total questions: 57

Worksheet time: 6hrs 26mins

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