Compound angle formulas
Use the compound angle (sum/difference) formulas to find the exact value of sin or cos at a non-special angle. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
Find the exact value of cos(30deg), using 30deg = 60deg - 30deg.
- √(3)/2
- √(6)/4 + √(2)/4
- 12
- √(2)/2
Answer: sqrt(3)/2
See one solved, step by step
Find the exact value of sin(30deg) using a compound angle formula.
- √(6)/4 + √(2)/4
- √(2)/2
- √(3)/2
- 12
📘 Worked solution
130deg = 60deg - 30degBreak the angle into two special angles whose sin and cos you know exactly.
2sin(A - B) = sin(A)cos(B) - cos(A)sin(B)This is the compound angle formula for sin.
3sin(30deg) = √(3)/2 · √(3)/2 - 12 · 12Substitute sin/cos of 60deg and 30deg from the special triangles.
4= 12Combine the two fractions over the common denominator 4.
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