Trigonometric Sum Identities

Question 1

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 2

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 3

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

Revolt · Accepted Answer

1; 0

Question 4

Which expression is equivalent to sin(84°)cos(43°) + cos(84°)sin(43°)?

Revolt · Accepted Answer

sin(127°)

Question 5

What is the exact value of sin(v + w), given , , v is an angle in Quadrant III, and w is an angle is Quadrant IV?

Revolt · Accepted Answer

StartFraction negative 30 + 4 StartRoot 21 EndRoot Over 55 EndFraction

Question 6

What is the exact value of sin(345°)?

Revolt · Accepted Answer

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

Question 7

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 8

Solve: for [, 2].

Revolt · Accepted Answer

StartFraction 5 pi Over 3 EndFraction

Question 9

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)

Question 10

If tan m = and tan n = –6, what is the exact value of tan(m + n)?

Revolt · Accepted Answer

Negative StartFraction 11 Over 8 EndFraction

Trigonometric Sum Identities Answers