Trigonometric Half Angle Identities

Question 1

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 2

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

Revolt · Accepted Answer

1-4-2-3-5

Question 3

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 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

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

Revolt · Accepted Answer

{0°, 60°, 300°}

Question 6

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

Revolt · Accepted Answer

1-3-4-2-5

Question 7

Which expression is equivalent to 2cos2?

Revolt · Accepted Answer

1

Question 8

What is the exact value of ?

Revolt · Accepted Answer

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

Question 9

What is the exact value of tan

Revolt · Accepted Answer

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

Question 10

Review the proof.

Revolt · Accepted Answer

sin(x)cos(x) + sin(x)

Trigonometric Half Angle Identities Answers