Free Printable Chapter 4: Trigonometric Functions

1.

Find the exact values of the six trigonometric functions of θ.

a)

sin θ = 4/5, sec θ = 5/4, cos θ = 3/5, csc θ = 5/3, tan θ = 3/4, cot θ = 3/4

b)

sin θ = 3/5, sec θ = 5/4, cos θ = 4/5, csc θ = 5/3, tan θ = 3/4, cot θ = 4/3

c)

sin θ = 3/5, sec θ = 5/3, cos θ = 4/5, csc θ = 5/4, tan θ = 3/4, cot θ = 4/3

d)

sin θ = 4/5, sec θ = 5/4, cos θ = 3/5, csc θ = 5/3, tan θ = 3/4, cot θ = 4/3

2.

Find the exact values of sin θ, cos θ, and tan θ for a right triangle where the length of the side opposite θ is 20 and the length of the side adjacent to θ is 21.

a)

sin θ = 20/29, cos θ = 21/29, tan θ = 20/21

b)

sin θ = 29/20, cos θ = 29/21, tan θ = 21/20

c)

sin θ = 21/29, cos θ = 20/29, tan θ = 20/21

d)

sin θ = 20/21, cos θ = 20/29, tan θ = 20/29

3.

Find the value of x.

a)

20.9

b)

36.6

c)

31.8

d)

27.6

4.

Change 10.625° to degrees, minutes, and seconds.

a)

10° 37' 50''

b)

10° 36' 50''

c)

10° 37' 30''

d)

10° 36' 30''

5.

Choose the angle measure represented by 5.2 rotations counterclockwise.

a)

1872°

b)

-936°

c)

-1872°

d)

936°

6.

Change -120° to radian measure in terms of $\pi$ .

a)

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

b)

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

c)

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

d)

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

7.

Find the measure of the reference angle of -200°.

a)

40°

b)

-200°

c)

160°

d)

20°

8.

Evaluate $\tan\frac{4\pi}{3}$ .

a)

$-\sqrt{3}$

b)

$-\frac{\sqrt{3}}{3}$

c)

$\sqrt{3}$

d)

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

9.

Find the exact value of $\csc\left(-\frac{3\pi}{2}\right)$ , if defined.

a)

-1

b)

0

c)

1

d)

undefined

10.

State the amplitude for the function $y=-\frac{2}{3}\cos\theta$ .

a)

-4/3

b)

2/3

c)

-2/3

d)

4/3

11.

Graph y = 5 cos 2θ for 1 period of the function.

a)

b)

c)

d)

12.

State the amplitude, period, phase shift, and vertical shift for $y=\cos\left(\theta-\pi\right)+2$ .

a)

1, 2𝝅, 𝝅, 2

b)

1, -2𝝅, -𝝅, 2

c)

-1, 2𝝅, 𝝅, -2

d)

1, -2𝝅, 𝝅, -2

13.

Find the period of the function y = csc(θ/4 - 𝝅/2) - 5.

a)

𝝅/2

b)

𝝅/3

c)

8𝝅

d)

4𝝅

14.

Sketch the graph of y = tan 3x.

a)

b)

c)

d)

15.

Which of the following is a vertical asymptote of y = tan 10x?

a)

10𝝅

b)

𝝅/20

c)

20𝝅

d)

𝝅/10

16.

Find the exact value of $\sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ , if it exists.

a)

4𝝅/3

b)

𝝅/6

c)

does not exist

d)

-𝝅/3

17.

Find the exact value of arcsin 4, if it exists.

a)

0

b)

1/4

c)

does not exist

d)

𝝅/4

18.

Find the exact value of arccos (1/2) if it exists.

a)

𝝅/6

b)

does not ecist

c)

𝝅/3

d)

5𝝅/6

19.

Solve ΔXYZ.

a)

∠Y = 105°, x ≈ 74.2, z ≈ 83.2

b)

∠Y = 105°, x ≈ 187.8, z ≈ 83.2

c)

∠Y = 105°, x ≈ 83.2, z ≈ 74.2

d)

∠Y = 105°, x ≈ 187.8, z ≈ 210.5

20.

For which of the following triangles is s = 10.5 in.?

a)

b)

c)

d)

Chapter 4: Trigonometric Functions

Total questions: 20

Worksheet time: 10mins

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