Free Printable Topic 7 - Trigonometric Functions

1.

Select all the possible measures for the angle shown.

a)

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

b)

$-210\degree$

c)

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

d)

$210\degree$

e)

$510\degree$

2.

An angle has a reference angle measuring 35° and its terminal side lies in Quadrant IV. What are possible positive and negative measures for the angle?

a)

325°, −35°

b)

35°, −145°

c)

35°, −325°

d)

145°, −35°

3.

Find the measure of an angle that is positive and less than 360° in standard position for each reference angle.

68° in quadrant II: (a) °

75° in quadrant IV: (b) °

22° in quadrant III: (c) °

Choose from the below words

112

285

202

45

150

270

4.

Convert the angle measures $\frac{\pi}{6}$ radians and $\frac{5\pi}{3}$ radians to degrees.

$\frac{\pi}{6}$ radians = (a) °

$\frac{5\pi}{6}$ radians = (b) °

Choose from the below words

30

150

60

225

300

5.

What are the sine and cosine of $\frac{2\pi}{3}$ ?

sin $\frac{2\pi}{3}$ = (a) cos $\frac{2\pi}{3}$ = (b)

Choose from the below words

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

$-\frac{1}{2}$

\frac{1}{2}

-\frac{\sqrt[]{3}}{2}

\sqrt[]{3}

4

6.

What is sin θ if cos θ = 12/13 and θ is in Quadrant IV?

a)

sin θ = 12/13

b)

sin θ = -5/13

c)

sin θ = 5/13

d)

sin θ = -12/13

7.

Select all the correct statements.

a)

$\tan\ \left(-\frac{4\pi}{3}\right)=-\sqrt[]{3}$

b)

$\cos\left(-\frac{7\pi}{3}\right)=-\frac{\sqrt[]{2}}{2}$

c)

$\cot\left(-\frac{11\pi}{3}\right)=-\frac{\sqrt[]{3}}{3}$

d)

$\sec\left(\frac{7\pi}{6}\right)=-\frac{2\sqrt[]{3}}{3}$

e)

$\sin\left(\frac{13\pi}{6}\right)=\frac{1}{2}$

8.

Using a two-way radio, Melissa can talk to anyone within an 8-mile radius of her location. Oscar is 30° west of south of Melissa’s location. What is Oscar’s exact location, relative to Melissa’s location, at the greatest distance where they can talk using two-way radios?

( (a) , (b) )

Choose from the below words

-4

$-4\sqrt[]{3}$

2\sqrt[]{3}

-3\sqrt[]{4}

3

-2

9.

Select all the correct statements.

a)

The amplitude of $y=2\cos\left(\frac{1}{2}x\right)\ is\ \frac{1}{2}$

b)

The period of $y=2\cos\left(\frac{1}{2}x\right)\ is\ \pi$

c)

The amplitude of $y=\frac{\pi}{2}\sin\left(\frac{\pi}{2}x\right)\ is\ \frac{\pi}{2}$

d)

The period of $y=4\pi\sin\left(\frac{1}{2}x\right)\ is\ 4\pi$

e)

The period of $y=\cos\left(2\pi x\right)\ is\ 1$

10.

What is the average rate of change of the function y = 3 sin(2x) on the interval $\left[0,\ \frac{\pi}{4}\right]$ ?

a)

$-\frac{12}{\pi}$

b)

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

c)

$\frac{6}{\pi}$

d)

$\frac{12}{\pi}$

11.

The equation for f and the graph of g are given. How do the period and the amplitude of the functions compare?

a)

The amplitudes are the same, but the period of f is half as long as the period of g .

b)

The amplitudes are the same, but the period of f is twice as long as the period of g .

c)

The periods are the same, but the amplitude of f is half as great as the amplitude of g

d)

The periods are the same, but the amplitude of f is twice as great as the amplitude of g .

12.

High tides at a beach occur at intervals of 12 hours 25 minutes. Yesterday, high tide was measured at 5 feet above sea level and low tide was measured at 1 foot above sea level. What is the amplitude of a cosine function modeling the depth of the water in feet as a function of time in hours?

13.

Select all the correct statements about the graphs of $y=\frac{1}{2}\sin x\ and\ y=\frac{1}{2}\sin\left(x-\frac{\pi}{2}\right)$

a)

The graph of $y=\frac{1}{2}\sin\left(x-\frac{\pi}{2}\right)$ is shifted $\frac{\pi}{2}$ units left from the graph of $y=\frac{1}{2}\sin x$

b)

The graph of $y=\frac{1}{2}\sin\left(x-\frac{\pi}{2}\right)$ is shifted $\frac{\pi}{2}$ units right from the graph of $y=\frac{1}{2}\sin x$

c)

The period of $y=\frac{1}{2}\sin\left(x-\frac{\pi}{2}\right)\ is\ \frac{\pi}{2}$ , and the period of $y=\frac{1}{2}\sin x\ is\ 2\pi$

d)

The amplitude of $y=\frac{1}{2}\sin\left(x-\frac{\pi}{2}\right)$ is half the amplitude of $y=\frac{1}{2}\sin x$

e)

The amplitude of $y=\frac{1}{2}\sin\left(x-\frac{\pi}{2}\right)$ is the same as the amplitude of $y=\frac{1}{2}\sin x$

14.

Function f is a cosine function with period 8π , amplitude 3, and a local maximum at f(0) = −3 . What is the equation of the midline of the graph of f ?

15.

What is the phase shift of the graph of $y=-2\sin\left(\frac{3}{2}x-\frac{\pi}{2}\right)-4$ ?

a)

$\frac{\pi}{2}$ units right

b)

$\frac{\pi}{3}$ units right

c)

4 units right

d)

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

16.

Select all the statements that describe the key features of the graph of $y=2\cos\left[\frac{1}{2}\left(x+\frac{\pi}{4}\right)\right]+5$

a)

amplitude =5

b)

period = $4\pi$

c)

phase shift is $\frac{\pi}{4}$ units left

d)

phase shift is 5 units left

e)

vertical shift is 5 units up

17.

Select all the correct statements about the graph of y = tan x .

a)

The period of the function is π .

b)

The range of the function is $\left(-\frac{\pi}{2},\ \frac{\pi}{2}\right)$

c)

The function has vertical asymptotes whenever sin x = 0 .

d)

The function has zeros whenever cos x = 0 .

e)

The function is increasing everywhere in its domain.

18.

The graph of y = tan x is stretched vertically by a factor of 4 and compressed horizontally to have a period of π/3 . What is the equation of the new graph?

y = (a) tan (b)

Choose from the below words

4

3x

1/4

\frac{\pi}{3}x

3\pi x

\frac{1}{3}x

19.

Choose from cot x , sec x , and csc x to complete the sentences below.

The graph of y = 1/sin x is the same as the graph of y = (a) .

The graph of y = 1/cos x is the same as the graph of y = (b) .

The graph of y = cos x / sin x is the same as the graph of y = (c) .

Choose from the below words

csc x

sec x

cot x

sin x

cos x

tan x

20.

The function y = f(x) is a tangent or cotangent function and its graph is as shown.

What is the equation of this function? Use decimals rounded to one decimal place.

f(x) = (a) cot ( (b) x)

Choose from the below words

0.5

4

1

2

-2

1/4

Topic 7 - Trigonometric Functions

Total questions: 20

Worksheet time: 22mins

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