Use a compound angle formula to determine an exact value of sin 7p12

Question

Use a compound angle formula to determine an exact value of sin 7π12

Answer 1

7π/12 = (7π/12)(180°/π) = 105°

 

sin(7π/12) = sin(105°) = sin(60° + 45°)

 

                                          = sin60°cos45° + cos60°sin45°

 

                                          = (√3/2)(√2/2) + (1/2)(√2/2)

 

                                          = (√6 +√2)/4