AnswersPascua Algebra 2 B Fall 2026Radian Measure

Evaluating the Six Trigonometric Functions Answers

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1
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If , which expression is equivalent to ?

Question illustration
A
StartFraction 1 Over negative three-eighths EndFraction
Option A
B
Negative three-eighths + 1
Option B
C
StartRoot 1 + StartFraction (Negative eight-thirds) squared EndRoot
Option C
D
(Negative three-eighths) squared + 1
Option D
2
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Which Pythagorean identity is correct?

A
sine squared (theta) + 1 = cosecant squared (theta)
Option A
B
tangent squared (theta) + 1 = secant squared (theta)
Option B
C
1 minus cotangent squared (theta) = cosecant squared (theta)
Option C
D
1 minus cosine squared (theta) = tangent squared (theta)
Option D
3

The terminal side of an angle in standard position passes through P(–3, –4). What is the value of ?

Question illustration
A
tangent theta = Negative four-thirds
Option A
B
tangent theta = Negative three-fourths
Option B
C
Tangent theta = three-fourths
Option C
D
Tangent theta = four-thirds
Option D
4

Given that , what is the value of , for ?

Question illustration
A
Negative StartRoot 2 EndRoot
Option A
B
StartRoot 2 EndRoot
Option B
C
0
D
1
5

Three trigonometric functions for a given angle are shown below.What are the coordinates of point (x, y) on the terminal ray of angle , assuming that the values above were not simplified?

Question illustration
A
(–77, –36)
B
(–77, 36)
C
(–36, 77)
D
(36, –77)
6

If , which of the following represents an approximate value of , for ?

Question illustration
A
0.7660
B
0.8392
C
1.1916
D
1.4198
7

Given that , what is the value of , for ?

Question illustration
A
Negative StartFraction 35 Over 12 EndFraction
Option A
B
Negative StartFraction 12 Over 35 EndFraction
Option B
C
StartFraction 12 Over 35 EndFraction
Option C
D
StartFraction 35 Over 12 EndFraction
Option D
8

Keisha and David each found the same value for , as shown below, given .Keisha’s SolutionDavid’s SolutionWhose procedure is correct?

Question illustration
A
Keisha’s procedure is correct.
B
David’s procedure is correct.
C
Both procedures are correct.
D
Neither procedure is correct.
9

Fatima wants to find the value of , given . Which identity would be best for Fatima to use?

Question illustration
A
cosine theta = StartFraction 1 Over secant theta EndFraction
Option A
B
sine squared theta + cosine squared theta = 1
Option B
C
Cosecant theta = StartFraction r Over y EndFraction
Option C
D
1 + cotangent squared theta = cosecant squared theta
Option D
10

The point is the point at which the terminal ray of angle intersects the unit circle. What are the values for the cosine and cotangent functions for angle ?

Question illustration
A
cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative 1
Option A
B
cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = 1
Option B
C
cosine theta = StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative one-half
Option C
D
cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = one-half
Option D
11

The point P(x, y) lies on the terminal side of an angle = –60° in standard position. What are the signs of the values of x and y?

Question illustration
A
Both x and y are positive.
B
Both x and y are negative.
C
x is positive, and y is negative.
D
x is negative, and y is positive.
12

The point P(x, y) lies on the terminal side of an angle = in standard position. What are the signs of the values of x and y?

Question illustration
A
Both x and y are positive.
B
Both x and y are negative.
C
x is positive, and y is negative.
D
x is negative, and y is positive.
13

Given that , what is the value of , for ?

Question illustration
A
Negative StartRoot StartFraction 20 Over 29 EndFraction EndRoot
Option A
B
Negative StartFraction 20 Over 29 EndFraction
Option B
C
StartFraction 20 Over 29 EndFraction
Option C
D
StartRoot StartFraction 20 Over 29 EndFraction EndRoot
Option D
14

Based on Pythagorean identities, which equation is true?

A
sine squared theta minus 1 = cosine squared theta
Option A
B
secant squared theta minus tangent squared theta = negative 1
Option B
C
negative cosine squared theta minus 1 = negative sine squared theta
Option C
D
cotangent squared theta minus cosecant squared theta = negative 1
Option D
15

The terminal side of an angle in standard position passes through P(15, –8). What is the value of ?

Question illustration
A
sine theta = fifteen-seventeenths
Option A
B
sine theta = negative eight-seventeenths
Option B
C
sine theta = eight-seventeenths
Option C
D
sine theta = fifteen-seventeenths
Option D

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