100% Assignment: Trigonometric Half Angle Identities

Proof of cosine half-angle identity: Analyze the proof. Use the drop-down boxes to complete the sentences. The third line of this proof is known as the ___. identity of cosine. The justification for the fourth line is ___.

power reducing substitution

What is the exact value of tan(9pi/8)?

sqrt2 - 1

What is the exact value of sin⁡(157.5°)?

sqrt2 - sqrt2/2

Jacob performs the work shown to find tan 165 degrees. Observe Jacob's work. Use the drop down box to complete the statement. The error in Jacob's work is ____.

the cosine expressions are reversed.

What is the value of cos(x/2) if tan x = 1/2 and x is in quadrant III?

-sqrt5 - 2 sqrt5/10

Find the solution(s) to the equation sin(x/2) + cos x - 1 = 0 on the interval 0 ≤ x 2π. Check all that apply.

0, pi/3, 5pi/3

Which of these expressions is the simplified form of the expression (sin(x)/1-cos^2(x)) tan(x/2)?

1/1 + cos (x)

Solve the equation. cos(x/2) = cosx + 1 What are the solutions on the interval 0° ≤ x < 360°? Solutions: {___ degrees, ___ degrees}

120 180

Select the place in which an error first occurs in the proof of sin(t/2).

Statement 2

This proof shows the first five steps for verifying cot^2 (x/2) = cos x + 1/cos x - 1 Use the drop-down boxes to complete the steps of the proof.

Tangent half-angle identity 1+cos x 1-cos x