Trigonometric Half Angle Identities

Question 1

What is the exact value of sin(112.5°)?

Revolt · Accepted Answer

StartFraction StartStartRoot 2 + StartRoot 2 EndRoot EndEndRoot Over 2 EndFraction

Question 2

Which expression is equivalent to 4sin2(x) – 8sin2?

Revolt · Accepted Answer

4(cos(x) – cos2(x))

Question 3

For 0 ≤ ϴ < 2π, how many solutions are there to tan = sin(ϴ)? Note: Do not include values that are undefined for tan or sin(ϴ).

Revolt · Accepted Answer

3

Question 4

For 0 ≤ ϴ < 2π , what are the solutions to sin2(ϴ) = 2sin2 ?

Revolt · Accepted Answer

Left-brace 0, StartFraction pi Over 2 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace

Question 5

What is the exact value of sin(75°)?

Revolt · Accepted Answer

StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction

Question 6

Review the proof (not in order) of the identity.

Revolt · Accepted Answer

1-4-2-3-5

Question 7

What is the exact value of tan(67.5°)?

Revolt · Accepted Answer

StartStartRoot StartFraction 2 + StartRoot 2 EndRoot Over 2 minus StartRoot 2 EndRoot EndFraction EndEndRoot

Question 8

Which expression is equivalent to ?

Revolt · Accepted Answer

sin(5x)

Question 9

Review the proof of .

Revolt · Accepted Answer

step 5

Question 10

For 0° ≤ x < 360°, what are the solutions to sin + cos(x) – 1 = 0 ?

Revolt · Accepted Answer

{0°, 60°, 300°}

Trigonometric Half Angle Identities Answers