Free Printable Trigonometric Functions Assessment

1.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

2.

What is the period of this equation?

y = -5sin(3x)

a)

-5

b)

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

c)

$\frac{2\pi}{5}$

d)

3

3.

The value of $\sin^{-1}\left(-\frac{1}{2}\right)\$

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{6}$

c)

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

d)

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

4.

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

a)

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

b)

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

c)

$\frac{\pi}{6}$

d)

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

5.

$\sin^{-1}\left(\cos\pi\right)$

a)

0

b)

$\pi$

c)

$\frac{\pi}{2}$

d)

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

6.

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

a)

$\sqrt{3}$

b)

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

c)

$-\sqrt{3}$

d)

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

7.

What is the equation of the graph?

a)

$y=2\cos x$

b)

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

c)

$y=2\sin x$

d)

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

8.

What is the equation of the graph?

a)

$y=2\cos x$

b)

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

c)

$y=2\sin x$

d)

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

9.

What is the equation of the graph?

a)

$y=2\sin\ x$

b)

$y=\frac{1}{2}\sin\ x$

c)

$y=\ 2\sin\ 2x$

d)

$y=\ \sin\ \frac{1}{2}x$

10.

What is the period of the function graphed here?

a)

$4\pi$

b)

$2\pi$

c)

$\pi$

d)

$8\pi$

11.

$\cos\ 30\degree\times\sin\ 60\degree=....$

a)

$\frac{1}{2}$

b)

$\frac{1}{3}$

c)

$\frac{1}{4}$

d)

$\frac{3}{4}$

12.

Given that cos(x) = -2/3, then the sec(x) = ?

a)

$-\frac{2}{3}$

b)

$-\frac{3}{2}$

c)

$\frac{3}{2}$

d)

$\frac{2}{3}$

13.

Find secΘ.

a)

$\frac{17}{15}$

b)

$\frac{15}{17}$

c)

$\frac{8}{17}$

d)

$\frac{17}{8}$

14.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

15.

Which graph represents $y=\cos\ x$ for $90\degree\le x\le270\degree$

a)

b)

c)

d)

16.

Find the equation of the function graphed above.

a)

$y=-\cos4x$

b)

$y=\sin4\left(x-1\right)$

c)

$y=\frac{1}{4}\cos x+1$

d)

$y=\frac{1}{4}\sin x+1$

17.

What is the vertical shift of the graph?

a)

Down 1

b)

Down 5

c)

Down 3

d)

Down 4

18.

Write the equation of a cosine graph given the following:
Midline: y = 0
Amplitude = 3
Reflection over the x-axis
No Horizontal translation
Period = $\pi$

a)

$y=-3\cos2x$

b)

$y=-3\cos\pi x$

c)

$y=-3\cos x$

d)

$y=3\cos x+2$

19.

A trig function has an amplitude of 4 and a minimum value of 5. What is its maximum value?

a)

7

b)

9

c)

11

d)

13

20.

Find the trigonometric equation with parent function y=cosx, period $\pi$ , amplitude 3, horizontal translation $\frac{\pi}{4}$ , and vertical shift 5.

a)

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

b)

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

c)

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

d)

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

21.

$y=3\sin\left(2x\right)-2$ What are the maximum and minimum values of this function?

a)

A. maximum value = 1, minimum value = –5

b)

B. maximum value = 2, minimum value = –6

c)

C. maximum value = –5, minimum value = 1

d)

D. maximum value = –5, minimum value = 0

22.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

23.

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

a)

Multiply by √2

b)

Divide by √2

c)

It's the same length as the hypotenuse.

d)

Divide by 2

24.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

25.

What are a and b in this 30-60-90 triangle?

a)

b=3.5√3 a = 7√3

b)

b = 7 a = 7√2

c)

b = 7 a = 14

d)

b = 7√3 a = 14√3

26.

Find the exact value of the expression below:

\sin^{-1}\left(\frac{\sqrt{2}}{2}\right)

a)

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

b)

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

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{4}$

27.

$\theta=\frac{5\pi}{6}$ What is the degree measure of this angle?

a)

135

b)

150

c)

210

d)

120

28.

What is 240 degrees in radians?

a)

$\frac{\pi}{3}$

b)

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

c)

$\frac{5\pi}{3}$

d)

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

29.

Which of the following is closest to the measure of the angle drawn by the green curve?

a)

5/6 π

b)

5/3 π

c)

4/5 π

d)

4/3 π

30.

Convert 100⁰ to radians

a)

$\frac{5\pi}{9}$

b)

$\frac{\pi}{2}$

c)

$\frac{5\pi}{8}$

d)

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

31.

Convert the following to degrees:

-8π/5 radians

a)

$-290\degree$

b)

$-260\degree$

c)

$-275\degree$

d)

$-288\degree$

32.

$y=-2\cos\left(b\left(x\right)\right)+2$

If the equation for this function is written as above, the value of b is (a) ?

33.

$y=2\cos\left(3\left(x-d\right)\right)+2$

If the equation for this function is written as above, the value of d is (a) ? (use "pi" to write your answer)

34.

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

If the equation for this function is written as above, the value of d is (a) ? (use "pi" to write your answer)

35.

Which of the following is the equation of the function graphed here?

a)

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

b)

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

c)

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

d)

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

e)

All of the above

36.

Solve sinθ = ½ on θ∈[0, 2π)

a)

θ = π / 6, 7π / 6

b)

θ = π / 6, 5π / 6

c)

θ = 5π / 6, 7π / 6

d)

θ = 7π / 6, 11π / 6

37.

Which of these is NOT
a solution to
tan θ = 0 ?

a)

θ = 0

b)

θ = π /2

c)

θ = π

d)

θ = 2π

38.

$\cos^2\theta=\frac{1}{2},\ 0\le\theta<2\pi$
Solve this equation for values of theta.

a)

$\theta=\frac{\pi}{4},\frac{7\pi}{4}$

b)

$\theta=\frac{\pi}{4},\frac{3\pi}{4}$

c)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

d)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

39.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

40.

Find the general solution of the equation.

a)

$\theta=\frac{\pi}{6}+2\pi n,\frac{11\pi}{6}+2\pi n$

b)

$\theta=\frac{\pi}{6}+\pi n$

c)

$\theta=\frac{5\pi}{6}+2\pi n,\frac{7\pi}{6}+2\pi n$

d)

$\theta=\frac{5\pi}{6}+\pi n$

Trigonometric Functions Assessment

Total questions: 40

Worksheet time: 1hrs 26mins

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