Exact Evaluation with Radians

  • 11th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
Review Board Member
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
 , MBA
By Thames
T
Thames
Community Contributor
Quizzes Created: 8157 | Total Attempts: 9,569,759
| Attempts: 14 | Questions: 20 | Updated: Dec 2, 2025
Please wait...
Question 1 / 21
🏆 Rank #-- ▾
Score 0/100
1) Evaluate cos(π/12) exactly.

Explanation

Think of π/12 as 15°. Cosine at 15° is the famous exact value with the plus sign.

Submit
Please wait...
About This Quiz
Exact Evaluation With Radians - Quiz

Are you ready to calculate exact values without the calculator? In this quiz, you’ll use sum and difference identities for sine, cosine, and tangent to evaluate tricky angles like 15°, 75°, and 105°. You’ll practice with both degrees and radians, seeing how radicals like √6 and √2 show up naturally.... see moreTake this quiz to sharpen your exact-value skills and make those “non-standard” angles feel easy.
see less

2)
You may optionally provide this to label your report, leaderboard, or certificate.
2) Evaluate cos(105°) 

Explanation

105° = 60° + 45°. Cosine of a sum gives the “√2 − √6 over 4,” which is the negative of (√6 − √2)/4

Submit
3) Evaluate sin(7π/12)

Explanation

7π/12 = 105°. Sine at 105° matches the “plus” one.

Submit
4) Evaluate cos(75°)

Explanation

75° = 45° + 30°. Cosine of a sum gives the “minus” one, positive.

Submit
5) Evaluate tan(5π/12)

Explanation

5π/12 = 75°. Tangent at 75° is the same large positive value.

Submit
6) Evaluate sin(165°)

Explanation

165° = 180° − 15°. Sine keeps the sin15° value (still positive).

Submit
7) Evaluate cos(165°)

Explanation

165° = 180° − 15°. Cosine flips sign of cos15°, giving the negative of the “plus” one.

Submit
8) Evaluate tan(165°)

Explanation

165° = 180° − 15°. Tangent picks up a minus: it’s −(2 − √3).

Submit
9) Evaluate sin(75°) exactly.

Explanation

75° = 45° + 30°. Use sine sum with the well-known 30°/45° values; it comes out to the “plus” one.

Submit
10) Evaluate tan(15°) exactly.

Explanation

15° = 45° − 30°. The tangent difference gives the small positive exact value.

Submit
11) Evaluate cos(15°)

Explanation

15° = 45° − 30°. Cosine at 15° is the “plus” value.

Submit
12) Evaluate sin(105°)

Explanation

105° = 60° + 45°. Sine of a sum gives the “plus” one.

Submit
13) Evaluate sin(5π/12)

Explanation

5π/12 = 75°. Sine at 75° is the “plus” one

Submit
14) Evaluate cos(5π/12)

Explanation

5π/12 = 75°. Cosine at 75° is the “minus” one, positive.

Submit
15) Evaluate tan(75°)

Explanation

75° = 45° + 30°. Tangent of a sum gives the large positive exact value.

Submit
16) Evaluate sin(15°)

Explanation

15° = 45° − 30°. Sine of a difference gives the small positive “minus” value.

Submit
17) Evaluate tan(105°)

Explanation

105° = 60° + 45°. Tangent of a sum gives the negative of 2 + √3.

Submit
18) Evaluate cos(11π/12)

Explanation

11π/12 = 165°. Cosine there is the negative of the 15° “plus” value.

Submit
19) Evaluate sin(11π/12)

Explanation

11π/12 = 165°. Sine there matches sin15° (positive small value).

Submit
20) Evaluate sin(-15°)

Explanation

−15° just flips sine’s sign from sin15°.

Submit
×
Saved
Thank you for your feedback!
View My Results
Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Evaluate cos(π/12) exactly.
Evaluate cos(105°) 
Evaluate sin(7π/12)
Evaluate cos(75°)
Evaluate tan(5π/12)
Evaluate sin(165°)
Evaluate cos(165°)
Evaluate tan(165°)
Evaluate sin(75°) exactly.
Evaluate tan(15°) exactly.
Evaluate cos(15°)
Evaluate sin(105°)
Evaluate sin(5π/12)
Evaluate cos(5π/12)
Evaluate tan(75°)
Evaluate sin(15°)
Evaluate tan(105°)
Evaluate cos(11π/12)
Evaluate sin(11π/12)
Evaluate sin(-15°)
play-Mute sad happy unanswered_answer up-hover down-hover success oval cancel Check box square blue
Alert!