Question

find the exact value of sin 11pi/12 using the sum or difference formula.

Answer 1

11/12 = 2/12 + 9/12 = 1/6 + 3/4
sin pi/6 = 1/2
cos pi/6 = (1/2) sqrt 3
sin 3 pi/4 = (1/2)sqrt 2
cos 3 pi/4 = -(1/2) sqrt 2

Answer 2

Some students feel more comfortable working with degrees.
sin(11π/12) = sin 165° = sin 15° by the CAST rule

sin15° = sin(45°-30°)
= sin45°cos30° - cos45°sin30°
= (√2/2)(√3/2) - (√2/2)(1/2)
= (√6 - √2)/4

sin 11π/12 = (√6-√2)/4