Free Printable Week 9: Review for Progress Check #3

1.

Based on the unit circle, what is the value of sin?

a)

y

b)

x

c)

x/y

d)

y/x

2.

Based on the unit circle, what is the value of cos?

a)

y

b)

x

c)

x/y

d)

y/x

3.

sin (π/2)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

4.

cos (π/4)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

5.

cos (π)

a)

√3/2

b)

-√2/2

c)

-1

d)

1

6.

cos (5π/3)

a)

-√2/2

b)

-1/2

c)

1/2

d)

√3/2

7.

tan (3π/4)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-1

8.

sin (-30^o)

a)

√3/2

b)

- 1/2

c)

1/2

d)

- √3/2

9.

cos (9π/4)

a)

√2/2

b)

√3/2

c)

1/2

d)

- √2/2

10.

sin (-7π/3)

a)

√2/2

b)

- √3/2

c)

- 1/2

d)

- √2/2

11.

The Pythagorean Theorem is
a² + b²+ c²

a)

false

b)

true

12.

What is always the longest side in a right triangle?

a)

leg (a)

b)

leg (b)

c)

hypotenuse (c)

d)

depends on the location of the right angle

13.

What side is the hypotenuse of the triangle?

a)

9

b)

40

c)

41

d)

none

14.

What is the to correct set up to find the value of X in the picture above?

a)

$12^2+20^2=X^2$

b)

$20^2+X^2=12^2$

c)

$X^2+12^2=20^2$

d)

$X^2+20^2=12^2$

15.

What is the length of the missing side?

a)

x = 4

b)

x = 8

c)

x = 10

d)

x = 16

16.

Solve for x:

a)

24

b)

19

c)

6

d)

12

17.

What is the ratio for Sine?

a)

$\frac{hyp}{opp}$

b)

$\frac{opp}{hyp}$

c)

$\frac{opp}{adj}$

d)

$\frac{adj}{opp}$

18.

What is the ratio for Cosine?

a)

$\frac{opp}{hyp}$

b)

$\frac{opp}{adj}$

c)

$\frac{adj}{opp}$

d)

$\frac{adj}{hyp}$

19.

What is $\cos A$ ?

a)

$\frac{29}{20}$

b)

$\frac{21}{29}$

c)

$\frac{20}{29}$

d)

$\frac{21}{20}$

20.

What is the ratio for Tangent?

a)

$\frac{opp}{hyp}$

b)

$\frac{adj}{opp}$

c)

$\frac{opp}{adj}$

d)

$\frac{hyp}{opp}$

21.

What is $\tan A$ ?

a)

$\frac{29}{20}$

b)

$\frac{21}{29}$

c)

$\frac{20}{29}$

d)

$\frac{21}{20}$

22.

The reciprocal of sine is

a)

cosine or cos

b)

secant or sec

c)

cosecant or csc

d)

arcsin or $\sin^{-1}$

23.

If $\sin\theta=\frac{4}{5}$ , then $\csc\theta=$

a)

$\frac{4}{5}$

b)

$-\frac{4}{5}$

c)

$-\frac{5}{4}$

d)

$\frac{5}{4}$

24.

The reciprocal of cosine is

a)

sine or sin

b)

secant or sec

c)

cosecant or csc

d)

arccos or $\cos^{-1}$

25.

If $\cos60\degree\ =\ \frac{1}{2}$ , then $\sec60\degree$ =

a)

$\frac{1}{2}$

b)

$2$

c)

$-\frac{1}{2}$

d)

$-2$

26.

The reciprocal of tangent is

a)

secant or sec

b)

cosecant or csc

c)

cotangent or cot

d)

arctan or $\tan^{-1}$

27.

If $\tan\theta=\frac{12}{5}$ , then $\cot\theta=$

a)

$-\frac{12}{5}$

b)

$\frac{12}{5}$

c)

$\frac{5}{12}$

d)

$-\frac{5}{12}$

28.

If $\sin x=\frac{3}{5}$ and $\cos x=\ \frac{4}{5}$ , what is the value of $\tan x$ ?

a)

$\frac{3}{4}$

b)

$\frac{4}{3}$

c)

$\frac{5}{5}$

d)

$\frac{7}{5}$

29.

If $\sin x=\frac{7}{25}$ and $\tan x=\ \frac{7}{24}$ , what is the value of $\sec x$ ?

a)

$\frac{24}{25}$

b)

$\frac{24}{7}$

c)

$\frac{25}{7}$

d)

$\frac{25}{24}$

30.

If $\sin x=\frac{8}{10}$ in the 2nd Quadrant , what is the value of $\tan x$ ?

a)

$\frac{6}{10}$

b)

$-\frac{6}{8}$

c)

$\frac{8}{6}$

d)

$-\frac{6}{10}$

31.

If $\cot x=\frac{8}{15}$ in the 3rd Quadrant , what is the value of $\cos x$ ?

a)

$\frac{8}{17}$

b)

$-\frac{15}{17}$

c)

$-\frac{8}{17}$

d)

$\frac{15}{17}$

32.

Which graph?

a)

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

b)

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

c)

$y=\sec\left(x\right)$

d)

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

33.

How can you restrict the domain to make $y=\cos x$ one-to-one?

a)

$0\ \ to\ \ \pi$

b)

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

c)

$-\pi\ \ to\ \ 0$

d)

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

34.

Which graph?

a)

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

b)

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

c)

$y=\sec\left(x\right)$

d)

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

35.

How can you restrict the domain to make $y=\sin x$ one-to-one?

a)

$0\ \ to\ \ \pi$

b)

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

c)

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

d)

$-\pi\ \ to\ \ 0$

36.

Which graph?

a)

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

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

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

37.

Which graph?

a)

$y=\csc\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\cot\left(x\right)$

d)

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

38.

Which graph?

a)

$y=\csc\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\cot\left(x\right)$

d)

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

39.

Which graph?

a)

$y=\csc\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\cot\left(x\right)$

d)

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

40.

Which of these trig functions has a period of

2\pi

?

a)

$y=\sin x$

b)

$y=\cos x$

c)

$y=\tan x$

d)

$y=\cot x$

e)

$y=\csc x$

41.

Which of these trig functions has a period of

\pi

?

a)

$y=\sin x$

b)

$y=\cos x$

c)

$y=\tan x$

d)

$y=\cot x$

e)

$y=\csc x$

42.

Which of these trig functions has a Domain of All Reals?

a)

$y=\sin x$

b)

$y=\cos x$

c)

$y=\tan x$

d)

$y=\cot x$

e)

$y=\sec x$

43.

Which of these trig functions has a Range of All Reals?

a)

$y=\sin x$

b)

$y=\cos x$

c)

$y=\tan x$

d)

$y=\cot x$

e)

$y=\sec x$

44.

Which of these trig functions has a vertical asymptote at x = $\pi$ ?

a)

$y=\sin x$

b)

$y=\csc x$

c)

$y=\tan x$

d)

$y=\cot x$

e)

$y=\sec x$

45.

How do you find the midline (or vertical shift) of a graph?

a)

max - min

b)

mid - min

c)

max - mid

d)

(max + min) / 2

46.

How do you find the amplitude of a graph?

a)

max - min

b)

mid - min

c)

max - mid

d)

(max + min) / 2

47.

What is the amplitude of this graph?

a)

-7

b)

-2

c)

3

d)

5

48.

The amplitude and equation of the midline are...

a)

amplitude: 1

midline: y = 2

b)

amplitude: 11

midline: y = 19

c)

amplitude: 30

midline: y = 8

d)

amplitude: 38

midline: y = 22

49.

Find the period of the graph shown.

a)

2

b)

4

c)

6

d)

8

50.

Which of the following equations represents the graph shown?

a)

y = 3 sin(π/4 x) + 2

b)

y = 3 cos(π/2 x) + 2

c)

y = 3 sin(π/2 x) + 2

d)

y = 3 cos(π/4 x) + 2

51.

What is the equation for this function?

a)

y=-22cos(2pi/15 x) + 12

b)

y=22 cos(2pi/15 x) + 12

c)

y= -22cos(15x)+12

d)

y= -22sin(2pi/15 x) + 12

52.

Which of the following equations represents the graph shown?

a)

y = 3 sin(π/4 x) + 2

b)

y = 3 cos(π/2 x) + 2

c)

y = 3 sin(π/2 x) + 2

d)

y = 3 cos(π/4 x) + 2

53.

A Ferris wheel has a diameter of 38 ft. The bottom of the Ferris wheel is 3 ft. off the ground and it makes one revolution every 30 seconds. After you board the Ferris wheel it takes you 14 seconds to get to the top. Which function could represent your height off the ground as a function of time (in seconds) as you ride the Ferris wheel?

a)

$y=38\cos\left(\frac{π}{15}(x–3)\right)+14$

b)

$y=38\cos\left(\frac{π}{30}\left(x-14\right)\right)+3$

c)

$y=19\cos\left(\frac{π}{30}(x–3)\right)+14\$

d)

$y=19\cos\left(\frac{π}{15}(x–14)\right)+3$

54.

Your height above the ground on a Ferris Wheel is modeled by the equation $y=-3\cos\left(\frac{\pi}{4}x\ \right)+4$ . How many seconds after the ride starts do you first reach a height of 4 feet?

a)

2

b)

7

c)

6

d)

4

55.

Which function could model the graph?

a)

arcsinx or sin^-1x

b)

arccosx or cos^-1x

c)

arctanx or tan^-1x

56.

Which function could model the graph?

a)

arcsinx or sin^-1x

b)

arccosx or cos^-1x

c)

arctanx or tan^-1x

57.

Which function could model the graph?

a)

arcsinx or sin^-1x

b)

arccosx or cos^-1x

c)

arctanx or tan^-1x

58.

Simplify

$\cot\theta\sin\theta$

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

59.

Simplify

$\tan x\csc x\cos x$

a)

1/cos x

b)

1

c)

cot x

d)

-1

60.

$1-\sin^2x\ =$

a)

$\sin^2x$

b)

$\cos^2x$

c)

$\sec^2x$

d)

$\csc^2x$

61.

$\sec^2x\ -\ 1\ =$

a)

$\cot^2x$

b)

$\csc^2x$

c)

$\cos^2x$

d)

$\tan^2x$

62.

Simplify $\left(\csc x+1\right)\left(\csc x-1\right)$

a)

$\csc^2x+1$

b)

$\tan^2x$

c)

$\cot^2x$

d)

$2\csc x$

63.

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$

a)

2secθ

b)

cot²θ

c)

tan²θ

d)

sec²θ + 1

64.

Use the unit circle to solve.

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

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{3}$

c)

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

d)

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

65.

Use the unit circle to solve.

$\sin x\left(\sin x-1\right)=0$

a)

0

b)

$\pi$

c)

$\frac{\pi}{2}$

d)

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

66.

$Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{4},\ \frac{\pi}{2},\ \frac{5\pi}{4},\ \frac{3\pi}{2}$

b)

$0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$

c)

$\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$

d)

$0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$

67.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$2\sin\theta\cos\theta-\sqrt{2}\cos\theta=0$

a)

$45\degree$

b)

$90\degree$

c)

$135\degree$

d)

$270\degree$

e)

$315\degree$

68.

Solve using the unit circle.

$\cos^2x=\cos x$

a)

0

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

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

69.

Which of the following is the same as $\cos\ \left(A+B\right)$

a)

$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$

b)

$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$

c)

$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$

d)

$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$

70.

Expand $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$

a)

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

b)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

c)

$\cos\ \frac{2\pi}{11}$

d)

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

71.

What is the value of $\sin\left(\pi+\theta\right)$ ,

if $\sin\theta=\frac{3}{10}$ ?

a)

$\frac{3}{10}$

b)

$\frac{\sqrt{91}}{10}$

c)

$-\frac{3}{10}$

d)

$-\frac{\sqrt{91}}{10}$

72.

What is the value of $\sin\left(\frac{\pi}{2}-\theta\right)$ ,

if $\sin\theta=\frac{5}{13}$ ?

a)

$\frac{5}{13}$

b)

$-\frac{5}{13}$

c)

$-\frac{12}{13}$

d)

$\frac{12}{13}$

73.

What is the value of $\cos\left(\pi-\theta\right)$ ,

if $\cos\theta=\frac{12}{13}$ ?

a)

$\frac{5}{13}$

b)

$-\frac{5}{13}$

c)

$-\frac{12}{13}$

d)

$\frac{12}{13}$

74.

What is the value of $\cos\left(\frac{3\pi}{2}+\theta\right)$ ,

if $\sin\theta=\frac{4}{5}$ ?

a)

$\frac{4}{5}$

b)

$-\frac{4}{5}$

c)

$\frac{3}{5}$

d)

$-\frac{3}{5}$

75.

What is the value of $\sin\left(\pi-\theta\right)$ ,

if $\sin\theta=\frac{3}{10}$ ?

a)

$\frac{3}{10}$

b)

$\frac{\sqrt{91}}{10}$

c)

$-\frac{3}{10}$

d)

$-\frac{\sqrt{91}}{10}$

Week 9: Review for Progress Check #3

Total questions: 75

Worksheet time: 4hrs 45mins

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