Advanced Functions (MHF4U) · Trigonometric Functions

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.

Practice this skill Curriculum: MHF4U-TF3.1

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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