Trigonometric Difference Identities

Question 1

A student uses the following steps to prove the sine sum identity. The proof is incorrect.Which step is incorrect?

Revolt · Accepted Answer

Step 4

Question 2

Oliver incorrectly states that the expression can be simplified as –1. Review Oliver’s work. = –1

Revolt · Accepted Answer

The expression does not simplify to –1.

Question 3

Which numbers complete the blanks when solving the equation over the interval [0, 2]?

Revolt · Accepted Answer

1; 0

Question 4

Review the steps in the derivation of the tangent sum identity. The steps are not in order.

Revolt · Accepted Answer

I IV II III

Question 5

Solve the equation over the interval [0, 2].

Revolt · Accepted Answer

StartFraction 5 pi Over 6 EndFraction and StartFraction 11 pi over 6 EndFraction

Question 6

What is the exact value of cos(195°)?

Revolt · Accepted Answer

StartFraction negative StartRoot 6 EndRoot minus StartRoot 2 EndRoot

Question 7

Solve: for [, 2].

Revolt · Accepted Answer

StartFraction 5 pi Over 3 EndFraction

Question 8

Which steps can be used to verify that tan(w + ) = tan(w)?

Revolt · Accepted Answer

Rewrite tan(w + ) using the tangent sum identity. Then simplify the resulting expression using tan() = 0.

Question 9

What is the exact value of sin(345°)?

Revolt · Accepted Answer

StartFraction negative StartRoot negative 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction

Question 10

Review the incomplete derivation of the cosine sum identity.Step 1Step 2Step 3 Step 4Step 5

Revolt · Accepted Answer

Step 3: Step 5: cos(x)cos(y) – sin(x)sin(y)

Trigonometric Difference Identities Answers