Free Printable 2019 Pre-Cal Fall Final Review

1.

Convert $\frac{7\pi}{6}$ to degrees.

a)

210°

b)

225°

c)

240°

d)

300°

e)

330°

2.

Convert $\frac{\pi}{5}$ to degrees.

a)

36°

b)

18°

c)

9°

d)

4.5°

e)

3°

3.

Convert 300° to radians.

a)

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

b)

$\frac{7\pi}{4}$

c)

$\frac{11\pi}{6}$

d)

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

e)

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

4.

Convert 15° to radians please.

a)

$\frac{\pi}{12}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{10}$

d)

$\frac{\pi}{20}$

e)

$\frac{\pi}{40}$

5.

What's the exact value of $\sin\left(30\degree\right)$

a)

$\frac{1}{2}$

b)

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

c)

$\frac{\sqrt{2}}{2}$

d)

$\sqrt{3}$

e)

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

6.

What's the exact value of $\cos\left(\frac{5\pi}{3}\right)$

a)

$\frac{1}{2}$

b)

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

c)

$\frac{\sqrt{2}}{2}$

d)

$\sqrt{3}$

e)

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

7.

What's the exact value of $\tan\left(\frac{7\pi}{4}\right)$

a)

$-1$

b)

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

c)

$1$

d)

$\sqrt{3}$

e)

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

8.

What's the exact value of $\sec\left(2\pi\right)$

a)

$-1$

b)

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

c)

$1$

d)

$\sqrt{3}$

e)

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

9.

What's the exact value of $\csc\left(150\degree\right)$

a)

2

b)

-2

c)

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

d)

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

e)

DNE

10.

Find the exact value of $\cot\left(\ \frac{3\pi}{2}\right)$

a)

0

b)

undefined

c)

1

d)

-1

e)

¯\_(ツ)_/¯

11.

$t$ is a real number and $P=\left(\frac{5}{6},-\frac{\sqrt{11}}{6}\right)$ is the point on the unit circle that corresponds to $t.$ What is the exact value of $\cos\left(t\right)?$

a)

$\frac{5}{6}$

b)

$\frac{6}{5}$

c)

$-\frac{\sqrt{11}}{6}$

d)

$-\frac{6\sqrt{11}}{11}$

e)

$-\frac{5\sqrt{11}}{11}$

12.

$t$ is a real number and $P=\left(\frac{5}{6},-\frac{\sqrt{11}}{6}\right)$ is the point on the unit circle that corresponds to $t.$ What is the exact value of $\cot\left(t\right)?$

a)

$\frac{5}{6}$

b)

$\frac{6}{5}$

c)

$-\frac{\sqrt{11}}{5}$

d)

$-\frac{6\sqrt{11}}{11}$

e)

$-\frac{5\sqrt{11}}{11}$

13.

$t$ is a real number and $P=\left(\frac{5}{6},-\frac{\sqrt{11}}{6}\right)$ is the point on the unit circle that corresponds to $t.$ What is the exact value of $\csc\left(t\right)?$

a)

$\frac{5}{6}$

b)

$\frac{6}{5}$

c)

$-\frac{\sqrt{11}}{5}$

d)

$-\frac{6\sqrt{11}}{11}$

e)

$-\frac{5\sqrt{11}}{11}$

14.

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

What is the Amplitude?

a)

2

b)

$-2$

c)

$\frac{\pi}{4}$

d)

$8$

e)

$-1$

15.

$2\sin\left(\frac{\pi}{4}x+\frac{\pi}{4}\right)+2$
What is the period?

a)

2

b)

$-2$

c)

$\frac{\pi}{4}$

d)

$8$

e)

$-1$

16.

$2\sin\left(\frac{\pi}{4}x+\frac{\pi}{4}\right)+2$
What is the phase shift?

a)

Left 2

b)

Right 2

c)

Right $\frac{\pi}{4}$

d)

Left 1

e)

Right 1

17.

$2\sin\left(\frac{\pi}{4}x+\frac{\pi}{4}\right)+2$
What is the vertical shift?

a)

Up 2

b)

Down 2

c)

Up $\frac{\pi}{4}$

d)

Up 1

e)

Down 1

18.

What's a possible equation of this function?

a)

$-2\sin\left(\frac{3}{2}x\right)$

b)

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

c)

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

d)

$-2\sin\left(\frac{2}{3}x\right)$

e)

$2\cos\left(x\right)+2$

19.

What's a possible equation of this function?

a)

$-2\cos\left(\frac{3}{2}x\right)$

b)

$2\cos\left(\frac{3}{2}x\right)$

c)

$-2\cos\left(\frac{2}{3}x\right)$

d)

$2\cos\left(\frac{2}{3}x\right)$

e)

$-2\sin\left(\frac{2}{3}x\right)$

20.

What's the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{5}$

e)

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

21.

What's the exact value of $\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{5}$

e)

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

22.

What's the exact value of $\tan^{-1}\left(\sqrt{3}\right)$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{5}$

e)

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

23.

What's the exact value of $\sin^{-1}\left(\cos\left(\frac{\pi}{6}\right)\right)$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{5}$

e)

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

24.

What's the exact value of $\cos\left(\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)$

a)

$\frac{\sqrt{2}}{2}$

b)

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

c)

$\frac{1}{2}$

d)

$1$

e)

$0$

25.

Simplify $\sin\theta\sec\theta$

a)

$\tan\theta$

b)

$\cot\theta$

c)

$2\sin\theta$

d)

$2\cos\theta$

e)

$\csc\theta$

26.

Simplify $\sec\theta\left(\cos\theta+\sin\theta\right)$

a)

$\tan\theta$

b)

$1+\tan\theta$

c)

$\cos\theta+\tan\theta$

d)

$\cos^2\theta$

e)

$2\cos\theta$

27.

Simplify $\cos\theta\tan\theta-\sin\theta\cos^2\theta$

a)

$\sin^3\theta$

b)

$3\sin\theta$

c)

$\tan^3$

d)

$\cos^3\theta$

e)

$3\cos\theta$

28.

Simplify $\csc\theta-\cot\theta\cos\theta$

a)

$\sin\theta$

b)

$\cos\theta$

c)

$\tan\theta$

d)

$\cot\theta$

e)

$\csc\theta$

29.

$\tan\theta-\sqrt{3}=0$

$0\le\theta<2\pi$
Which is NOT a solution to the equation?

a)

$\frac{\pi}{3}$

b)

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

c)

$\frac{7\pi}{3}$

30.

$2\sin^2\theta-3\sin\theta-2=0$

$0\le\theta<2\pi$
Which is NOT a solution to the equation?

a)

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

b)

$\frac{11\pi}{6}$

c)

$\frac{\pi}{6}$

31.

What's the general formula for the equation?
$\cos\left(3\theta\right)=-1$

a)

$\theta=\frac{\pi}{3}+\frac{2}{3}n\pi$

b)

$\theta=\pi+2n\pi$

c)

$\theta=\frac{\pi}{6}+\frac{1}{3}n\pi$

d)

$\theta=\frac{\pi}{2}+\frac{2}{3}n\pi$

32.

Which is NOT a general formula for the equation below?

$3\csc\theta-2\sqrt{3}=0$

a)

$\theta=\frac{\pi}{3}+2\pi n$

b)

$\theta=\frac{2\pi}{3}+2\pi n$

c)

$\theta=\frac{4\pi}{3}+2\pi n$

33.

$\angle\alpha=?$

a)

$36.9\degree$

b)

$53.1\degree$

c)

$48.6\degree$

d)

$41.4\degree$

e)

5

34.

side $c=?$

a)

$6.13$

b)

$5.39$

c)

$6.96$

d)

$7.13$

35.

side $c=?$

a)

34.886

b)

7.043

c)

4.104

d)

5.814

36.

$\angle A=?$

a)

42.849^o

b)

103.137^o

c)

45.573^o

d)

31.29^o

e)

98.357^o

37.

What's the area of the triangle?

a)

36.226

b)

20.444

c)

12.797

d)

12.075

38.

What's the area of the triangle?

a)

27.495

b)

66.422

c)

88.958

d)

24.62

39.

From a hot air balloon 100 meters high, the angle of depression to the top of a nearby statue is 58⁰. The angle of depression to the base of the statue is 64⁰. How tall is the statue?

a)

21.95 ft

b)

18.75 ft

c)

16.25 ft

d)

14.15 ft

40.

From a hot air balloon 150 meters high, the angle of depression to the top of a nearby statue is 57⁰. The angle of depression to the base of the statue is 65⁰. How tall is the statue?

a)

42.29

b)

43.89

c)

44.55

d)

47.95

2019 Pre-Cal Fall Final Review

Total questions: 40

Worksheet time: 3hrs 20mins

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