Find exact values without a calculator

Question

a. sin(2π/3)

b. cos (3π/4)

c. cos (11π/6)

Answer 1

a. sin(2π/3) =

sin(π - 2π/3) = using sin(x) = sin(π - x)

sin(π/3) = √3/2 using Pythagorean Theorem applied to half of an equilateral triangle

b. cos (3π/4) =

-cos(π - 3π/4) = using cos(x) = -cos(π - x)

-cos(π/4) = -√2/2 using Pythagorean Theorem applied to an isosceles triangle

c. cos (11π/6) =

cos(2π - 11π/6) = using cos(x) = cos(2π - x)

cos(π/6) = √3/2 using Pythagorean Theorem applied to half of an equilateral triangle