AnswersAlgebra 2 MP 234 CHSEvaluating the Six Trigonometric Functions

Evaluating the Six Trigonometric Functions Answers

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1
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Francesca drew point (–2, –10) on the terminal ray of angle , which is in standard position. She found values for the six trigonometric functions using the steps below.Step 1Step 2 Step 3Which of the following explains whether all of Francesca’s work is correct?

Question illustration
A
Each step is correct because she plotted the point, drew a line to the x-axis to form a right triangle, used the Pythagorean theorem to find the hypotenuse, and finally wrote the correct ratios for all six functions.
B
She made her first error in step 1 because she should have drawn the line to the y-axis to form the right triangle.
C
She made her first error in step 2 because she should have used a negative value for r.
D
She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.
2
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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.
3

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.
4

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
5

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
6

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
7

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
8

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.
9

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.
10

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

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