Give the exact value of cos (3𝜋/4 − 11𝜋/6)

Answer 1

cos(3π/4 - 11π/6) = cos(3π/4)cos(11π/6) + sin(3π/4)sin(11π/6) = (-√2/2)(√3/2) + (√2/2)(-1/2) = (-√6 - √2) / 4

Answer 2

3pi/4 - 11pi/6 = 9pi/12 - 22pi/12 = -13pi/12

cos(-13pi/12) = cos(11pi/12)= cos(165)= about-0.966

reference angle is 15 degrees or pi/12

use the half angle formula

cos(pi/6) = (1/2)sqr3, cos(5pi/6) =-(1/2)sqr3

cos(pi/12) = sqr(1/2+(sqr3)/4)

cos(11pi/12 = exactly -sqr(1/2+(sqr3)/4)