Trigonometric Half Angle Identities

Question 1

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 2

Which expression is equivalent to ?

Revolt · Accepted Answer

– 1 + cos(ϴ)

Question 3

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

Revolt · Accepted Answer

StartFraction StartStartRoot 2 + StartRoot 2 EndRoot EndEndRoot Over 2 EndFraction

Question 4

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 5

What is the exact value of ?

Revolt · Accepted Answer

Negative StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction

Question 6

Which expression is equivalent to 2cos2?

Revolt · Accepted Answer

1

Question 7

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

Revolt · Accepted Answer

4(cos(x) – cos2(x))

Question 8

Review the proof of .

Revolt · Accepted Answer

step 5

Question 9

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 10

What is the exact value of sin(75°)?

Revolt · Accepted Answer

StartFraction StartStartRoot 2 + StartRoot 3 EndRoot EndEndRoot Over 2 EndFraction

Trigonometric Half Angle Identities Answers