Free Printable Chapter 4B Trig Test

1.

State the amplitude, period, and phase shift of the function $y=4\sin\left(2x-\frac{\pi}{3}\right)$

a)

Amp: 4 ; period: $\pi$ ; phase shift: $\frac{\pi}{6}$ right

b)

Amp: 4 ; period: $2\pi$ ; phase shift: $\frac{\pi}{6}$ left

c)

Amp: 4 ; period: $\pi$ ; phase shift: $\frac{\pi}{3}$ right

d)

Amp: 4 ; period: $\frac{\pi}{2}$ ; phase shift: $\frac{\pi}{3}$ left

2.

State the amplitude, period, and phase shift of the function $y=\frac{1}{2}\cos\left(\frac{x}{3}+\pi\right)$

a)

Amp: $\frac{1}{2}$ ; period: $6\pi$ ; phase shift: $3\pi$ left

b)

Amp: $\frac{1}{2}$ ; period: $3\pi$ ; phase shift: $\pi$ left

c)

Amp: $\frac{1}{2}$ ; period: $\frac{\pi}{6}$ ; phase shift: $3\pi$ right

d)

Amp: $\frac{1}{2}$ ; period: $6\pi$ ; phase shift: $\frac{\pi}{3}$ left

3.

Write an equation of the sine function with amplitude of 4, period $\pi$ , and phase shift $\frac{\pi}{2}$ to the right.

a)

$y=4\sin\left(2x-\pi\right)$

b)

$y=4\sin\left(2x+\frac{\pi}{2}\right)$

c)

$y=4\sin\left(x-\frac{\pi}{2}\right)$

d)

$y=4\sin\left(2x+\pi\right)$

4.

Write an equation of the cosine function with amplitude of $\frac{2}{3}$ , period $\frac{\pi}{4}$ , and vertical shift $5$ units down.

a)

$y=\frac{2}{3}\cos\left(8x\right)-5$

b)

$y=\frac{2}{3}\cos\left(4x\right)-5$

c)

$y=\frac{2}{3}\cos\left(\frac{x}{4}\right)-5$

d)

$y=\frac{2}{3}\cos\left(8x\right)+5$

5.

Which of the following could be the equation of the graph shown?

a)

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

b)

$y=2\cos x$

c)

$y=2\cos\left(\frac{x}{2}\right)$

d)

$y=2\sin2x$

6.

Which of the following could be the equation of the graph shown?

a)

$y=2\cos\left(4x\right)+1$

b)

$y=2\cos\left(\frac{x}{4}\right)+1$

c)

$y=2\cos\left(\frac{x}{2}\right)+1$

d)

$y=-3\sin\left(\frac{x}{4}\right)+1$

7.

Which of the following could be the equation of the graph shown?

a)

$y=\sin\left(2x\right)+1$

b)

$y=2\sin2x$

c)

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

d)

$y=\cos\left(4x\right)+1$

8.

Which of the following could be the equation of the graph shown?

a)

$y=3\sin\left(\frac{x}{2}\right)+2$

b)

$y=5\sin2x$

c)

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

d)

$y=3\cos\left(\frac{1}{2}x\right)+2$

9.

$y=\tan\left(2x-\frac{\pi}{3}\right)$ State the period and phase shift of the function

a)

Period: $\pi$ , phase shift: $\frac{\pi}{6}$ right

b)

Period: $\frac{\pi}{2}$ , phase shift: $\frac{\pi}{6}$ right

c)

Period: $\pi$ , phase shift: $\frac{\pi}{3}$ right

d)

Period: $\frac{\pi}{2}$ , phase shift: $\frac{2\pi}{3}$ right

10.

Write an equation of a tangent function with a period of $\frac{\pi}{2}$ and a phase shift of $\pi$ to the left.

a)

$y=\tan\left(2x+2\pi\right)$

b)

$y=2\tan\left(x-\pi\right)$

c)

$y=\tan\left(2x-\pi\right)$

d)

$y=\tan\left(4x+\pi\right)$

11.

Which equation matches the graph shown?

a)

$y=2\tan\ \left(\frac{x}{2}\right)$

b)

$y=2\tan x$

c)

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

d)

$y=\tan\left(\frac{x}{2}\right)$

12.

Evaluate: $\sin^{-1}\left(\frac{1}{2}\right)$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{3}$

d)

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

13.

Evaluate: arctan(1)

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{4}$

c)

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

d)

$\frac{\pi}{6}$

14.

Evaluate: $\arccos\left(-\frac{\sqrt{3}}{2}\right)$

a)

-π/6

b)

-π/3

c)

2π/3

d)

5π/6

15.

Evaluate: sin^-1(cos π/3)

a)

π/6

b)

π/3

c)

1/2

d)

√3/2

16.

What range of angles can you get from inverse sine?

a)

0 to π

b)

0 to 2π

c)

-π/2 to π/2

d)

π/2 to 3 π/2

17.

What range of angles can you get from inverse cosine?

a)

0 to π

b)

0 to 2π

c)

-π/2 to π/2

d)

π/2 to 3 π/2

18.

sin^-1[cosπ]

a)

0

b)

π

c)

π/2

d)

-π/2

19.

arccos(cos 5π/4)

a)

3π/4

b)

2π/3

c)

5π/4

d)

-4π/5

20.

Evaluate: $\tan^{-1}\left(\sqrt{3}\right)$

a)

$\frac{\pi}{6}$

b)

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

c)

$\frac{\pi}{3}$

d)

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

21.

$\cot\left(\arcsin\left(\frac{3}{4}\right)\right)$ Evaluate:

a)

$\frac{\sqrt{7}}{3}$

b)

$\frac{3\sqrt{7}}{7}$

c)

$\frac{5}{3}$

d)

$\frac{4}{5}$

22.

Evaluate: $\cos\left(\arctan\left(\frac{3}{4}\right)\right)$

a)

$\frac{\sqrt{7}}{3}$

b)

$\frac{3\sqrt{7}}{7}$

c)

$\frac{5}{3}$

d)

$\frac{4}{5}$

23.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse?

a)

25 feet

b)

45 feet

c)

110 feet

d)

135 feet

24.

Kevin leans a 16 foot ladder l against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

a)

39.6

b)

6.0

c)

14.8

d)

13.6

25.

Elizabeth is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63.6 ft

b)

1.59 ft

c)

74.2 ft

d)

86.9 ft

26.

Jasmea is flying a plane. After takeoff, it flies in a straight line for a distance of 4000 feet in order to gain an altitude of 800 feet. Find the angle of elevation from the ground to the plane. Round to the nearest degree.

a)

78 degrees

b)

I love Math

c)

12 degrees

d)

11 degrees

27.

An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to be 16.5° and 10.5° respectively. How long is the island to the nearest foot?

a)

2807 ft.

b)

3225 ft

c)

1987 ft.

d)

2744 ft

28.

Determine the possible equation of the graph:

a)

$y=\tan\left(2\cdot x\right)+2$

b)

$y=\tan\left(\frac{\pi}{2}x\right)+2$

c)

$y=\tan\left(x\right)+\frac{\pi}{2}$

d)

$y=\tan\left(x\right)+2$

29.

Which could be the equation of the graph?

a)

$y=\tan3x$

b)

$y=-\tan3x$

c)

$y=-3\tan x$

d)

$y=-2\tan\ \left(\frac{1}{3}x\right)$

30.

Which could be the equation of the tangent graph?

a)

$y=3\tan\left(\frac{1}{2}x\right)$

b)

$y=\tan\left(\frac{1}{2}x\right)$

c)

$y=3\tan\left(2x\right)$

d)

$y=3\tan x$

Chapter 4B Trig Test

Total questions: 30

Worksheet time: 2hrs 32mins

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