Evaluating the Six Trigonometric Functions

Question 1

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?

Revolt · Accepted Answer

(36, –77)

Question 2

Given that , what is the value of , for ?

Revolt · Accepted Answer

StartRoot 2 EndRoot

Question 3

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?

Revolt · Accepted Answer

x is positive, and y is negative.

Question 4

Given that , what is the value of , for ?

Revolt · Accepted Answer

Negative StartFraction 12 Over 35 EndFraction

Question 5

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?

Revolt · Accepted Answer

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.

Question 6

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?

Revolt · Accepted Answer

x is negative, and y is positive.

Question 7

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 ?

Revolt · Accepted Answer

cosine theta = Negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction, cotangent theta = negative 1

Question 8

If , which expression is equivalent to ?

Revolt · Accepted Answer

StartFraction 1 Over negative three-eighths EndFraction

Question 9

Based on Pythagorean identities, which equation is true?

Revolt · Accepted Answer

cotangent squared theta minus cosecant squared theta = negative 1

Question 10

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

Revolt · Accepted Answer

Both procedures are correct.

Evaluating the Six Trigonometric Functions Answers

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