wayground logo

Free Printable Worksheets

Font size

S
M
L
XL
Worksheets

Amnesty_Unit 2 Inverse Trig Functions

Total questions: 100

Worksheet time: 4hrs 39mins

Name
Class
Date
1.

What is the acronym to help you remember the ratios to use in trigonometry?

a)

RIGHTANG

b)

SOHCAHTOA

c)

SHOCHATOA

d)

SAHCOHTOA

2.
What is the side across from the right angle called?
a)
Leg
b)
Pythagoras
c)
Hypotenuse
d)
Altitude
3.
We can use SOH-CAH-TOA for...
a)
Any triangle ever
b)
Non-right triangles only
c)
Right Triangles only
d)
Never
4.

What does CAH stand for

a)

cosine is the adjective over the hypotenuse.

b)

cosine is the adjacent side over the hypotenuse side.

c)

cosine is the adjacent side over the hippopotamus.

d)

cosine is the hypotenuse side over the adjacent side.

5.
What does SOH stand for
a)
hypotenuse over opposite
b)
adjacent over opposite
opposite over adjacent
c)
opposite over hypotenuse
d)
adjacent over adjacent
6.

What is the correct ratio you would use to solve for "w"?

a)

sin 40 = w/28

b)

cos 40 = w/28

c)

tan 40 = w/28

d)

sin 40 = 28/w

7.
Which trig function would you use with this diagram?
a)
Sin
b)
Cos
c)
Tan
d)
Wha??
8.

Find the length of side AB.

a)

20 m

b)

5 m

c)

11.54 m

d)

8.66 m

9.

Solve for the missing distance.

a)

18.9

b)

19.5

c)

47.3

d)

27.5

10.
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)
63.6 ft
b)
1.59 ft
c)
74.2 ft
d)
86.9 ft
11.

sin⁡ 38°=x42\sin\ 38\degree=\frac{x}{42}   Solve the equation for x.

Round your answer to the nearest tenth.



(a)  

12.

Solve the equation for x.

cos⁡ 28°=x+39\cos\ 28\degree=\frac{x+3}{9} Round your answer to the nearest tenth.



(a)  

13.

Solve the equation for x.

tan⁡ 41°=28x\tan\ 41\degree=\frac{28}{x}

Round your answer to the nearest tenth.

(a)  

14.

What is used to find missing angle measures of right triangles?

a)

Pythagorean Theorem

b)

Inverse Trig Functions

15.
Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle
a)
32°
b)
44°
c)
61°
d)
50°
16.
Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle
a)
33°
b)
49°
c)
39°
d)
41°
17.

Find the measure of theta

a)

40

b)

39

c)

90

d)

55

18.

Determine the measurement of the missing angle

a)

90º

b)

37°

c)

36°

d)

10º

19.
What is the radius of a unit circle?
a)
1
b)
2
c)
1/2
d)
0
20.
What are the coordinates of 60° on the unit circle?
a)
(0, 1)
b)
(1/2, √3/2)
c)
(√3/2, 1/2)
d)
(√2/2, 1/2)
21.
sinθ is positive in
a)
the 1st and 2nd quadrants
b)
the 1st and 3rd quadrants
c)
the 1st and 4th quadrants
d)
the 2nd and 3rd quadrants
22.
cosθ is positive in
a)
the 1st and 2nd quadrants
b)
the 1st and 3rd quadrants
c)
the 1st and 4th quadrants
d)
the 2nd and 3rd quadrants
23.
What is the exact coordinates of  3π/4 on the unit circle?
a)
(−√2∕2, √2∕2)
b)
(−√2∕2, −√2∕2)
c)
(−√3∕2, −√2∕2)
d)
(√2∕2, −√2∕2)
24.

Secant, or sec, is the reciprocal of (a)   .

25.

Cotangent, or cot, is the reciprocal of (a)   .

26.

Cosecant, or csc, is the reciprocal of (a)   .

27.

Find θ\theta   on the interval [0, 2π):

2csc⁡ x +17 = 15+csc⁡ x2\csc\ x\ +17\ =\ 15+\csc\ x

1st: ISOLATE csc x by ADDING/SUBTRACTING, then MULTIPLYING/DIVIDING

"csc x = ????"

2nd: Use an Unit Circle to find answer(s)

a)
7π/6
b)
11π/6
c)
7π/6; 11π/6
d)
7π/6+2πn; 11π/6+2πn
28.
What is the exact value of sin 150°
a)
-1/2
b)
-√3/2
c)
1/2
d)
√3/2
29.
sinθ is positive in
a)
the 1st and 2nd quadrants
b)
the 1st and 3rd quadrants
c)
the 1st and 4th quadrants
d)
the 2nd and 3rd quadrants
30.
cosθ is positive in
a)
the 1st and 2nd quadrants
b)
the 1st and 3rd quadrants
c)
the 1st and 4th quadrants
d)
the 2nd and 3rd quadrants
31.
What is the exact coordinates of  3π/4 on the unit circle?
a)
(−√2∕2, √2∕2)
b)
(−√2∕2, −√2∕2)
c)
(−√3∕2, −√2∕2)
d)
(√2∕2, −√2∕2)
32.
What is the value of cosine at 270
a)
0
b)
1
c)
-1
33.
At what point are sine and cosine the same value?
a)
0
b)
90
c)
45
d)
60
34.
a)
1
b)
-1
c)
0
d)
√2/2
35.

What are the 3 basic trig functions?

a)

Sine, cosine, and cotangent

b)

Sine, cotangent, and cosecant

c)

Sine, cosine, and tangent

d)

Cosecant, cosine, and cotangent

36.
Choose the best match for the graph.
a)
30o
b)
45o
c)
60o
d)
90o
37.
Choose the best match for the graph.
a)
30o
b)
45o
c)
60o
d)
90o
38.
Choose the best match for the graph.
a)
30o
b)
45o
c)
60o
d)
90o
39.
What is the angle measure, in degrees, at the red marking on the unit circle?
a)
30°
b)
45°
c)
60°
d)
90°
40.
Evaluate the function:  arcsin(-1/2)
a)
π/3
b)
π/6
c)
5π/6
d)
-π/6
41.
Evaluate: Csc-1(-√2)
a)
π/4
b)
3π/4
c)
-π/4
d)
-3π/4
42.

Which equation is true?

a)

sin (x) = 11/27

b)

sin (x) = 27/11

c)

cos (x) = 11/27

d)

tan (x) = 11/27

43.

Which equation is true?

a)

sin (x) = 6/8

b)

cos (x) = 8/6

c)

cos (x) = 6/8

d)

tan (x) = 6/8

44.

Which equation would you use to solve for the unknown angle?

a)

x = sin–1(4/5)

b)

x = cos–1(4/5)

c)

x = cos–1(5/4)

d)

x = tan–1(4/5)

45.
What is the RANGE of angles for inverse sine?
a)
[0, π]
b)
[-1, 1]
c)
[-π/2, π/2]
d)
(-∞, ∞)
46.
What RANGE of angles for inverse cosine?
a)
[0, π]
b)
(-∞, ∞)
c)
[-π/2, π/2]
d)
[-1, 1]
47.
What is the RANGE of angles for inverse tangent?
a)
[-π/2, π/2]
b)
(-π/2, π/2)
c)
[0, π]
d)
(-∞, ∞)
48.
What is the period
of
 y = 3 sin 2x?
a)
2
b)
3
c)
180
d)
360
49.
What is the amplitude of y = 3 cos 2x?
a)
3
b)
2
c)
90
90⁰
d)
350⁰
50.

Check all that apply to  F(x)=Tan(x)F\left(x\right)=Tan\left(x\right)  

a)

Tan(x)Tan\left(x\right)  has a restricted domain: −π2<x<π2-\frac{\pi}{2}<x<\frac{\pi}{2}  

b)

Tan−1(x)Tan^{-1}\left(x\right)  exists

c)

its range is  [−1,1]\left[-1,1\right]  

d)

Tan(−π4)=−1Tan\left(-\frac{\pi}{4}\right)=-1  

e)

The domain is restricted to QI and QIV on the unit circle.

51.
Choose the correct ratio.
a)
A
b)
B
c)
C
d)
D
52.
If you are given the opposite side and hypotenuse, which trig function should you use?
a)
sine
b)
cosine
c)
tangent
d)
cotangent
53.

Find tangent of θ.

a)

8/12

b)

23/12

c)

8/23

d)

12/23

54.

Use SOHCAHTOA to solve for the missing side. Round your answer to the nearest tenth.

a)

44.6

b)

22.7

c)

41.7

d)

38.5

55.

Use SOHCAHTOA to solve for the missing side. Round your answer to the nearest tenth.

a)

46.1

b)

4.9

c)

16.4

d)

26.9

56.

Find the measure of the missing angle. Round your answer to the nearest tenth.

a)

49.5o

b)

0.99o

c)

40.5o

d)

33.0o

57.

Use SOHCAHTOA to solve for the missing side. Round your answer to the nearest tenth.

a)

7

b)

6.3

c)

13.6

d)

7.8

58.
The amplitude of y = 4Cos(2x) is...
a)
4
b)
2
c)
8
d)
1
59.

Which function represents the graph?

a)

f(x) = 3 sin x

b)

f(x) = 3 cos x

c)

f(x) = -3 sin x

d)

f(x) = -3 cos x

60.

From the perspective of angle  θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

61.

From the perspective of angle  θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

62.

From the perspective of angle θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

63.
Find the value of tan A.
a)
17/8
b)
17/15
c)
8/17
d)
8/15
64.
Find the value of cos X.
a)
3/5
b)
3/4
c)
4/5
d)
4/3
65.
Find the value of sin Z.
a)
17/8
b)
8/15
c)
17/15
d)
15/17
66.
Find the value of cos X.
a)
3/4
b)
4/5
c)
5/4
d)
4/3
67.
Which trig ratio would you use to solve for x?
a)
tangent
b)
cosine
c)
radians
d)
sine
68.
What side does x represent?
a)
hypotenuse
b)
right angle
c)
adjacent
d)
opposite
69.
Which equation would be used to solve for x?
a)
tan 44 = x/15
b)
cos 44 = x/15
c)
cos 44 = 15/x
d)
tan 44 = 15/x
70.
Which is the correct set up to solve for x?
a)
sin 24 = x / 12
b)
cos 24 = x / 12
c)
tan 24 = x / 12
71.

From the perspective of angle  θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

72.

From the perspective of angle θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

73.

From the perspective of angle θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

74.

From the perspective of angle θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

75.

From the perspective of angle θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

76.

From the perspective of angle θ\theta , which trig ratio would correctly compare the 2 sides identified with stars?

a)

Sin

b)

Cos

c)

Tan

77.

Which of these is equivalent to 2cos2x − 3cosx = 0 ?

a)

-cos2x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

78.

Which is a correct way to solve the equation

cosx(2cosx − 3) = 0?

a)

divide cos x from both sides

b)

set each factor equal to 0 and solve

c)

distribute cosx into the parentheses

d)

guess and hope for the best

79.

Why doesn't 2cosx − 3 = 0 have solutions?

a)

cos x is never bigger than one

b)

cos x is never equal to a fraction

c)

Actually, this equation does have a solution, x = π

d)

This equation will have a solution tomorrow.

80.

Choose a good way to start solving this equation

tanx sin2x = 2 tanx

a)

divide tanx from both sides

b)

factor out tanx

c)

subtract 2 tanx from the left and then factor tanx out

d)

cancel sin2x out

81.

So tanx sin2x = 2 tanx is equivalent to tanx(sin2x − 2) = 0

Then tanx = 0 or sin2x − 2 = 0, now what?

a)

solutions come only from tanx = 0,

b)

solutions come only from sin2x − 2 = 0

c)

solutions come from where sin x is undefined

d)

solutions come from where tan x is undefined

82.

The square root of 2 is bigger than 1.

a)

true

b)

false

83.

To solve this equation, cos2x + sinx = 1, replace cos2x with

a)

1/(sec2x)

b)

sin2x − 1

c)

1 − sin2x

d)

1 + tan2x

84.

Organize this equation so it can be factored:

1−sin2x + sinx = 1

a)

move all to the right: 0 = sin2x − sinx

b)

cancel the ones and cancel a sinx

c)

replace sin2x with 1 − cos2x

d)

use this: 0 = sin2x − sinx + 2

85.

Factor 0 = sin2x − sinx

a)

0 = sinx(sinx)

b)

0 = sinx(1 − sinx)

c)

0 = cosx(sinx − 1)

d)

0 = sinx(sinx − 1)

86.

On the domain [0, 2π), solve this equation 0 = sinx(sinx − 1)

a)

0, π

b)

0, π, ½π

c)

½π

d)

0, 90, 270

87.

csc2x = 2 is equivalent to sin2x = ½

a)

True

b)

False

88.

To solve the equation sec2x − secx = 2

a)

start by subtracting 2 from both sides and then factor

b)

add sec x to both sides and factor

c)

factor out secx and set each factor equal to 2

d)

sec x is never bigger than 1, so there are no solutions

89.

Factor: sec2x − secx − 2

a)

(sec x)(secx − 2)

b)

(secx − 2)(secx − 1)

c)

(secx − 2)(secx + 1)

d)

(secx + 2)(secx − 1)

90.

Solve the equation (secx − 2)(secx + 1) = 0 on [0, 3600)

a)

60⁰, 180⁰, 300⁰

b)

30⁰, 180⁰,330⁰

c)

60⁰, 120⁰

d)

180⁰

91.

The goal of solving a one, two, or multi-step equations is to:

a)

Find the constant

b)

Find the coefficient

c)

Find the value of the variable

d)

Guess and check

92.

What is the first step to solve this equation?
x - 5 = 7 - 2x

a)

Add 7 to both sides of the equation

b)

Add 2x to both sides of the equation

c)

Subtract 2x from both sides of the equation

d)

Subtract 5 from both sides of the equation

93.

What is the next step to solve this equation?
3x - 5 = 7

a)

Add 5 to both sides of the equation

b)

Add 3x to both sides of the equation

c)

Subtract 5 from both sides of the equation

d)

Subtract 7 from both sides of the equation

94.

In the equation


x + 7 = 12


7 is being added to the variable, x.

How should you show your work to isolate the variable and solve the equation?

a)

Subtract 7 from both sides. The solution is x = 5.

b)

Add 7 to both sides.

The solution is x = 19.

c)

Multiply both sides by 7 The solution is x = 84.

95.

16 =k1116\ =\frac{k}{11}  


The variable, k, is being divided by 11. What step needs to be completed to isolate the variable k?

a)

Divide both sides by 11

b)

Multiply both sides by 11.

c)

Add 11 to both sides.

d)

Subtract 11 to both sides.

96.

What is the solution of 6d = 24

a)

d = 4

b)

d = 5

c)

d = 18

d)

d = 144

97.
3 + 12(3p + 2) = 9(p - 3)
a)
-20
b)
-13
c)
-2
d)
-18
98.
-12(x - 1) = -3(x - 1)
a)
10
b)
1
c)
14
d)
23
99.
−3(10 + 4v) = −6(5 − 9v)
a)
22
b)
-14
c)
0
d)
20
100.
What is the amplitude of the graph? 
a)
1
b)
3
c)
6
d)
9

Similar Resources on Wayground

ÔN TẬP GIỮA HK1 TOÁN 10

100 questions

ÔN TẬP GIỮA HK1 TOÁN 10

quiz

Worksheet

•

10th Grade

Midterm Review

95 questions

Midterm Review

quiz

Worksheet

•

11th Grade

Flashcard Set #3 - exponents fundamentals

100 questions

Flashcard Set #3 - exponents fundamentals

quiz

Worksheet

•

6th Grade - University

Hon IM1 Semester 2 Review

100 questions

Hon IM1 Semester 2 Review

quiz

Worksheet

•

9th - 12th Grade

Math 8 Review The 100

103 questions

Math 8 Review The 100

quiz

Worksheet

•

7th - 10th Grade

Algebra 1st Semester Review

100 questions

Algebra 1st Semester Review

quiz

Worksheet

•

8th - 12th Grade

Teoria de exponentes

97 questions

Teoria de exponentes

quiz

Worksheet

•

9th - 12th Grade

Matematik Tahap 2 (W2)

100 questions

Matematik Tahap 2 (W2)

quiz

Worksheet

•

1st - 10th Grade