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Worksheets

PC EC

Total questions: 66

Worksheet time: 2hrs 2mins

Name
Class
Date
1.
In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...
a)
Multiply that leg by 2
b)
Use the same length for the second leg
c)
Multiply that leg by √2
d)
Divide that leg by √2
2.
What is the length of y in this picture?
a)
45
b)
5√2
c)
90
d)
5
3.
Which side is the short leg of this 30-60-90 triangle?
a)
6
b)
m
c)
n
4.
What is the length of x in this 45-45-90 triangle?
a)
4√2
b)
4
c)
8
d)
4√3
5.
Which side is the long leg in this 30-60-90 triangle?
a)
4
b)
u
c)
v
6.
What is the length of y in this 45-45-90 triangle?
a)
8√2
b)
4√2
c)
4
d)
8
7.
What equation can be used to solve for x?
a)
Sin(40°)= x/40 
b)
Sin(40º)=x/19
c)
Cos(40º)=x/19
d)
Tan(40°)=19/x
8.
Solve for the misssing distance
a)
18.9
b)
19.5
c)
47
d)
27.5
9.
Find x round to the nearest tenth.
a)
46.1
b)
4.9
c)
16.4
d)
26.9
10.
Solve for x. Round to the nearest tenth.
a)
103.5
b)
4.7
c)
55.0
d)
23.4
11.
If an angle is rotated x degrees and the terminal point is (5, -12), then what is the value of sinx?
a)
12/13
b)
-12/13
c)
5/13
d)
-12/5
12.
If an angle is rotated x degrees and the terminal point is (-3,4), then what is the value of sinx?
a)
-3/5
b)
4/5
c)
-4/3
d)
5/4
13.
If an angle is rotated x degrees and the terminal point is (-3,4), then what is the value of secx
a)
-5/4
b)
-4/3
c)
5/4
d)
-5/3
14.
If an angle is rotated x degrees and the terminal point is (7,24), then what is the value of cscx?
a)
24/25
b)
25/24
c)
7/25
d)
25/7
15.
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
16.
The hypotenuse of any right triangle from the center of the unit circle to an edge is always
a)
1
b)
sqt2/2
c)
sqt3/2
d)
1/2
17.
Based on your unit circle sin(30o)=
a)
sqt2/2
b)
1/2
c)
1
d)
sqt3/2
18.
Based on your unit circle cos(90o)=
a)
1
b)
0
c)
-1
d)
1/2
19.
sin π/4
a)
√2∕2
b)
1/2
c)
√3/2
d)
0
20.
cos 5π/6
a)
-1/2
b)
1/2
c)
√3/2
d)
-√3/2
21.
cot 3π/4
a)
-√2/2
b)
-1
c)
1
d)
√2/2
22.
tan (-π)
a)
undefined
b)
0
c)
1
d)
-1
23.
Find a coterminal angle to 100 degrees.
a)
820
b)
720
c)
360
d)
390
24.
Find a coterminal angle to 45 degrees.
a)
360
b)
405
c)
315
d)
295
25.
Find a coterminal angle to -27 degrees.
a)
-387
b)
27
c)
323
d)
-393
26.
In which quadrant would you find an angle measuring -740°
a)
1
b)
2
c)
3
d)
4
27.
Find a coterminal angle to 3π/2
a)
-90
b)
90
c)
-270
d)
300
28.
In which quadrant would you find an angle measuring - 13π / 5
a)
1
b)
2
c)
3
d)
4
29.
tan 7π/4
a)
-1
b)
1
c)
√2/2
d)
undefined
30.
Convert 100⁰ to radians
a)
5π/9
b)
π/2
c)
5π/8
d)
5π/6
31.
Co-terminal angles for 10o, include:
a)
350o, -pi/18, 17pi/18, and -370o
b)
-350o, pi/18, -17pi/18, and 370o
c)
350o, pi/18, 17pi/18, and 370o
d)
-350o, -pi/18, -17pi/18, and -370o
32.
Name one positive coterminal angle to 80°
a)
280°
b)
440°
c)
180°
d)
360°
33.
Name a negative coterminal angle to π/6
a)
-11π/6
b)
-5π/6
c)
11π/6
d)
7π/6
34.
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
35.
Solve on the Interval [0,2π)
tan(x)+1=2
a)
0 and π  
b)
3π/4 and 7π/4
c)
π/4 and 5π/4
d)
3π/4 and 5π/4
36.
Solve on the interval [0,360)
2cosx-1=0
a)
60,120
b)
60, 240
c)
120, 240
d)
60, 300
37.
Solve
2cos2θ -1=0
on θ∈[0, 2π)
a)
θ = π /4, 7π /4
b)
θ = π /4, 3π /4
c)
θ = 3π /4, 5π /4
d)
θ = π /4, 3π /4, 5π /4, 7π /4
38.
TRUE or FALSE: 
sin(2x) = 2sin(x)
a)
TRUE
b)
FALSE
39.
Find the measure of the angle.  Round to the nearest tenth. 
a)
40.4
b)
43.4
c)
48.2
d)
41.3
40.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

41.

Going clockwise around the unit circle gives you a....

a)

sad feeling

b)

negative angle

c)

positive angle

d)

smile

42.

Going counterclockwise around the unit circle gives you a....

a)

ticket to a rock concert

b)

negative angle

c)

nightmare

d)

positive angle

43.

Coterminal angles are...

a)

angles that end in the same place

b)

angles that add up to 360°

c)

angles that add up to 180°

d)

angles that are complimentary

44.

Choose ALL that are correct!!!!!

To find a coterminal angle, you can...

a)

multiply by π/180

b)

subtract 360°

c)

add 360°

d)

add 180°

45.

CLICK ALL CORRECT ANSWERS!!!

Reference angles...

a)

are the smallest angle between the terminal side and the x-axis

b)

are always positive

c)

are less than 90°

d)

are less than or greater than 90°

46.

What is the sine trigonometric function for the given theta?

a)

20/29

b)

29/21

c)

21/20

d)

21/29

47.

Convert 225° to radian measure

a)
b)
c)
d)
48.
You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. What is the approximate height of the pick? (hint: use 30-60-90 theorems)
a)
32√3
b)
16√3
c)
32
d)
16√2
49.
A 40 foot ladder which is leaning against a wall reaches the wall at a point 36 feet above the ground. Find the measure of the angle created between the ladder and the ground. Round to the nearest degree
a)
64 degrees
b)
26 degrees
c)
42 degrees
d)
I love Math!
50.
Tangent is...
a)
a. Opposite/hypotenuse
b)
b. sine/cosine
c)
c. neither a or b
d)
d. both a and b
51.
What is cscθ?
a)
3/4
b)
4/3
c)
5/3
d)
5/4
52.
Given the Cos(x) = -2/3, then the Sec(x) = ?
a)
-2/3
b)
-3/2
c)
3/2
d)
2/3
53.
*
a)
cos x
b)
csc x
c)
sec x
d)
cot x
54.

Given cos⊖ = √3/2 , find the exact value for tan⊖

a)

(-2√3)/3

b)

(2√3)/3

c)

2

d)

√3/3

55.
Evaluate sec(7π/6)
a)
-1/2
b)
-2
c)
-√3/2
d)
-2√3 / 3
56.
Evaluate cot(3π/2)
a)
0
b)
-1
c)
undefined 
d)
1
57.
a)
Undefined
b)
0
c)
1
d)
-1
58.
Which of these is NOT
 a solution to
tan θ = 0 ?
a)
θ = 0
b)
θ = π /2
c)
θ = π
d)
θ = 2π
59.

Find sec θ if cot θ = 5√11 / 11

a)

7/25

b)

6√11 / 11

c)

6/5

d)

5√11 / 11

60.

Given the point (-2, √5) is on the terminal side of angle R, what is the value for cscR?

a)

√5/3

b)

√5/-2

c)

-2/3

d)

3√5/5

61.

Which is the proper assortment for Reciprocal Functions?

a)

sin & csc, cos & sec, tan & cot

b)

sin & cos, sec & csc, tan & cot

c)

sin & sec, cos & csc, tan & cot

d)

this & that, those & these, them & they

62.

Given sinA=5/13, and A is in Quadrant I, what is the value of tanA?

a)

5/12

b)

13/5

c)

12/5

d)

12/13

63.
Which of the following is a negative coterminal angle of 165 degrees? 
a)
-165
b)
525
c)
-525
d)
-555
64.
What are the negative and positive coterminal angles of 240 degrees?
a)
540°, -120°
b)
600°, -120°
c)
425°, -240°
d)
120°, -135°
65.
Given sin(θ) = 3/5 and 90 ≤ θ ≤ 180, what is cot(θ)?
a)
4/5
b)
-4/5
c)
-4/3
d)
4/3
66.
What quadrant does sin θ >0, cos θ < 0
a)
Quadrant I
b)
Quadrant II
c)
Quadrant III
d)
Quadrant IV

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