Cosine Half Angle

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 6941 | Total Attempts: 9,517,194
| Questions: 20
Please wait...
Question 1 / 20
0 %
0/100
Score 0/100
1) Which formula expresses cos(θ/2)?
Submit
Please wait...
About This Quiz
Cosine Half Angle - Quiz

Did you know you can find the cosine of half an angle using only the full angle? In this quiz, you’ll practice applying and proving the half-angle formula for cosine, while working with exact values, identities, and quadrant reasoning. We bring you this quiz to help you connect formulas to... see morereal computations. see less

2)
We’ll put your name on your report, certificate, and leaderboard.
2) If cos θ = 3/5 and θ is in quadrant IV, find cos(θ/2).
Submit
3) If θ = 150°, compute cos(θ/2) exactly.
Submit
4) Simplify (1 + cosθ)/2.
Submit
5) Derive cos(θ/2) from cos(2x).
Submit
6) If cos θ = −12/13 and θ is in quadrant II, find cos(θ/2).
Submit
7) Which quadrant contains θ/2 if θ = 240°?
Submit
8) Simplify cos²(θ/2) + sin²(θ/2).
Submit
9) If θ = 120°, what is cos(θ/2)?
Submit
10) If cos θ = 0 and 0 < θ < π, compute cos(θ/2).
Submit
11) Which identity is correct for cos²(θ/2)?
Submit
12) If θ = 90°, compute cos(θ/2).
Submit
13) Which identity is equivalent to cos(θ/2)?
Submit
14)  If cosθ = 0.6 and 0 < θ < π, compute cos(θ/2) in simplest radical form.
Submit
15)  If θ = 300°, determine the sign of cos(θ/2).
Submit
16) Which identity equals cos(θ/2)·sin(θ/2)?
Submit
17) If sin θ = 24/25 in quadrant I, compute cos(θ/2).
Submit
18) Simplify (1−cosθ)/2.
Submit
19) If θ = 45°, compute cos(θ/2).
Submit
20)  If cos(θ/2) = 3/5 and θ/2 is in Quadrant I, find cosθ
Submit
View My Results

Quiz Review Timeline (Updated): Oct 12, 2025 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Oct 12, 2025
    Quiz Edited by
    ProProfs Editorial Team
  • Sep 30, 2025
    Quiz Created by
    Thames
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Which formula expresses cos(θ/2)?
If cos θ = 3/5 and θ is in quadrant IV, find cos(θ/2).
If θ = 150°, compute cos(θ/2) exactly.
Simplify (1 + cosθ)/2.
Derive cos(θ/2) from cos(2x).
If cos θ = −12/13 and θ is in quadrant II, find cos(θ/2).
Which quadrant contains θ/2 if θ = 240°?
Simplify cos²(θ/2) + sin²(θ/2).
If θ = 120°, what is cos(θ/2)?
If cos θ = 0 and 0 < θ < π, compute cos(θ/2).
Which identity is correct for cos²(θ/2)?
If θ = 90°, compute cos(θ/2).
Which identity is equivalent to cos(θ/2)?
 If cosθ = 0.6 and 0 < θ < π, compute...
 If θ = 300°, determine the sign of cos(θ/2).
Which identity equals cos(θ/2)·sin(θ/2)?
If sin θ = 24/25 in quadrant I, compute cos(θ/2).
Simplify (1−cosθ)/2.
If θ = 45°, compute cos(θ/2).
 If cos(θ/2) = 3/5 and θ/2 is in Quadrant I, find...
Alert!

Back to Top Back to top
Advertisement