cos(-11pi/12)

Answer 1

sometimes I find it easier to visualize these kind of angles in degrees
π/12 radians = 15°,
so -11π/12 = -165°
and 165 = 120+45

cos(-11π/12) = cos(-165° = cos(165°)
= cos(120 + 45)
= cos120cos45 - sin120sin45
= (-1/2)(1/√2) - (√3/2)(1/√2)
= (-1 - √3)/(2√2)
or
= (-√2 - √6)/4