Free Printable Trigonometric Ratios and Unit Circle Plus Spiral Review

1.

What is the side length that is adjacent to $\angle$ J?

a)

9

b)

40

c)

41

d)

none

2.

What is the length of the hypotenuse?

a)

16

b)

30

c)

34

d)

17

3.

What is the side length that is opposite $\angle$ J?

a)

9

b)

40

c)

41

d)

none

4.

Which is the correct ratio for the cosine ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

5.

Which is the correct ratio for the sine ratio?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

6.

Which is the correct ratio for tangent?

a)

$\frac{adjacent\ }{hypotenuse}$

b)

$\frac{opposite\ }{hypotenuse}$

c)

$\frac{adjacent\ }{opposite\ }$

d)

$\frac{opposite\ }{adjacent\ }$

7.

What is sin(B)?

a)

a/c

b)

b/c

c)

a/b

d)

b/a

8.

What is the correct ratio?

a)

9/41

b)

40/41

c)

9/40

d)

40/9

9.

tan_____ = $\frac{30}{16}$

a)

X

b)

Y

c)

Z

d)

$90\degree$

10.

sin _____ = $\frac{16}{34}$

a)

X

b)

Y

c)

Z

d)

$90\degree$

11.

Solve for x. Round to the nearest tenth.

a)

9.8

b)

0.1

c)

0.038

d)

9.9

12.

Solve for x. Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

23.4

13.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

14.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

73.5

d)

68.6

15.

A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an angle of $74^o$ with the level ground. How high on the wall does the ladder reach?

a)

20.15 ft

b)

22.67 feet

c)

25.63 feet

d)

15.36 feet

16.

Susan 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 ft

b)

65 ft

c)

74 ft

d)

87 ft

17.

The unit circle...

a)

Has center at (1,1)

b)

Has a circumference of 1

c)

Has a diameter of 1

d)

Has a radius of 1

18.

Based on your unit circle sin(30^o)=

a)

sqt2/2

b)

1/2

c)

1

d)

sqt3/2

19.

What is 90° in radians?

a)

1/2

b)

π/2

c)

2/3

d)

2π/3

20.

What is 45° in radians?

a)

1/4

b)

π/4

c)

2/5

d)

2π/5

21.

What is 36° in radians?

a)

1/5

b)

π/5

c)

1/3

d)

π/3

22.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

23.

Convert $\frac{π}{3}$ from radians to degrees

(type number only)

(a)

24.

To convert from degrees to RADIANS

a)

multiply by

\frac{π}{180°}

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

25.

To convert from radians to DEGREES

a)

multiply by

\frac{π}{180°}

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

26.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

27.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

28.

a)

1

b)

-1

c)

0

d)

√2/2

29.

a)

√3/3

b)

√3

c)

1

d)

undefined

30.

a)

½

b)

√2/2

c)

√3/2

d)

1

31.

What is the Amplitude of the graph?

a)

3

b)

6

c)

12

d)

$2\pi$

32.

What is the Period of the graph?

a)

3

b)

$\pi$

c)

6

d)

$2\pi$

33.

$5\sin\left(2x-1\right)+4$

What is the amplitude in the function

a)

5

b)

$2\pi$

c)

$\frac{\pi}{2}$

d)

4

34.

$5\sin\left(2x-1\right)+4$

What is the period in the function?

a)

5

b)

$2\pi$

c)

$\pi$

d)

4

35.

What is the amplitude of the graph?

a)

8

b)

4

c)

$\frac{\pi}{3}$

d)

$6\pi$

36.

What is the midline in the graph?

a)

y=1

b)

y=0

c)

y=3

d)

y=2

37.

What function is this?

a)

y=-sin(x)

b)

y=sin(x)

c)

y=2sin(x)

d)

y=0.5sin(x)

38.

The period of a sine or cosine graph can be found by ....

a)

It's always 2π

b)

2π/B

c)

B(2π)

d)

2π+B

39.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

40.

Which equation?

a)

y= -cos(2x)

b)

y= cos(2x)

c)

y= (1/2)cosx

d)

y= (-1/2)cosx

41.

Write the equation for a sine function with an amplitude of 6 and a period of π/4.

a)

y=6sin(8x)

b)

y=6sin8(x-1)

c)

y=6sin1/4x

d)

y=6sinx

42.

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = sin (3 x)

d)

f(x) = cos (3 x)

43.

What is the domain and range of y=sinx?

a)

D: (-∞, ∞)
R: [-1, 1]

b)

D: (-∞, ∞)
R: [-π, π]

c)

D: (∞, -∞)
R: [-1, 1]

d)

D: (-∞, ∞)
R: [-∞, ∞]

44.

The period of a function is

a)

how long one cycle is before the function repeats

b)

how high and low the function goes from the center line

c)

the range of the function

45.

Select the cosine graph.

a)

b)

c)

46.

What is the amplitude of the given graph?

(a)

47.

Which choice(s) below are NOT true about the parent functions for Sine (y = sin x) and Cosine (y = cos x)?

a)

They have the same max and min values

b)

They both have the same period

c)

They both have the same y-intercepts

d)

They both have the same midlines

e)

They both have the same amplitude

48.

What did Jack break when he fell down from the hill?

a)

His pail of water

b)

His bucket

c)

Jill's Crown

d)

Jack's Crown

49.

How many continents are on this planet?

a)

5

b)

6

c)

7

d)

8

50.

What is the State Motto of North Carolina?

a)

Esse Quam Videri

b)

The People Rule

c)

Justitia Omnibus

d)

Ad Astra Per Aspera

51.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

52.

Which of the following graphs has the largest average rate of change from -1 to 2?

a)

b)

c)

d)

53.

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

a)

Arithmetic

b)

Geometric

c)

Neither

54.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

55.

What is the 9^th term in a geometric sequence with a common ratio of 2 and a first term of 3?

a)

384

b)

768

c)

1,536

d)

27

56.

Which explicit formula describes the sequence?

$-1,\ 3,\ 7,\ 11,\ ...$

a)

$a_n=4+\left(n-1\right)\left(-1\right)$

b)

$a_n=\left(4\right)\left(-1\right)^{n-1}$

c)

$a_n=-1+\left(n-1\right)\left(4\right)$

d)

$a_n=\left(-1\right)\left(4\right)^{n-1}$

57.

In a geometric sequence, a₁ = 486 and a₂ = 162. What is the explicit formula for this sequence?

a)

a_n = 2(3)^n-1

b)

a_n = 18(3)^n-1

c)

a_n = 18(1/3)^n-1

d)

a_n = 486(1/3)^n-1

58.

In an arithmetic sequence, the third term is 1 and the ninth is 49. What is the explicit formula for the sequence?

a)

a_n = 8n − 15

b)

a_n = −8n − 15

c)

a_n = 8n − 23

d)

a_n = −8n − 23

59.

$s_n=\frac{n}{2}\left[2a_1+\left(n-1\right)d\right]$

Use the formula for the following. Both formulas given should produce the same sum.

The sum $s_{82}$ for the sequence
-9 -3 +3+9+15+...

a)

18,891

b)

81,891

c)

19,881

d)

19,188

60.

concavity

a)

concave up only

b)

concave down only

c)

both concave up and down

d)

none

61.

Which best describes the change in the average rate of change?

a)

It is increasing at an increasing rate.

b)

It is increasing at a decreasing rate.

c)

It is decreasing at an increasing rate.

d)

It is decreasing at a decreasing rate.

62.

Is this graph concave up, down, or neither?

a)

Concave Up

b)

Concave Down

c)

Neither

63.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

64.

What are the equations of the asymptotes of the given graph

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x= -2, y = 1

c)

x=2 and y= -1

d)

x=1, y =2, y = -2

65.

What is the slant (Oblique) asymptote for the equation

f(x) = (x² - 4x + 2)/(x + 3)

a)

y = x -1

b)

y = x -7

c)

y = -7x + 23

d)

y = -2x + 2

66.

Which one means the function goes up on the left

a)

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

67.

Which one means the function goes down on the left

a)

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$

b)

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty$

68.

Which is the correct notation for the "limit of f(x) as x approaches 3 is 7"?

a)

$\lim_{x\rightarrow7}f\left(x\right)=3$

b)

$\lim_{ }f\left(3\right)=7$

c)

$f\left(3\right)=7$

d)

$\lim_{x\rightarrow3}f\left(x\right)=7$

69.

$\lim_{x\rightarrow-\infty}f\left(x\right)=\ ?$

a)

$-\infty$

b)

$\infty$

c)

$0$

d)

$10$

70.

Which notation means "to the right"?

a)

$\lim_{x\rightarrow-\infty}$

b)

$\lim_{x\rightarrow\infty}$

c)

$f\left(x\right)=-\infty$

d)

$f\left(x\right)=\infty$

71.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

72.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

73.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

74.

Which of the following represents the exponential equation?

a)

$y=mx+b$

b)

$y=a\left(b\right)^x$

c)

$y=ax^2+bx+c$

d)

none of the above

75.

$6\ +\ \log_2\ x\ =\ 6$

a)

9

b)

$\frac{1}{10}$

c)

1

d)

121

Trigonometric Ratios and Unit Circle Plus Spiral Review

Total questions: 75

Worksheet time: 2hrs 1mins

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