How would you solve this?

Question

How would you solve cos((5(pie))/6)

WITHOUT CALCULATOR

Answer 1

Well, 5π/6 is a 2nd quadrant angle and π/6 is
your reference angle, so
cos(5π/6) = -cos(π/6).
Also, you know sin(π/6) = 1/2.
(In a 30,60, 90 right triangle, the side opposite
the 30 degree angle is half the hypotenuse.)
Thus, cos(π/6) = √(1 - 1/4) = √3/2
cos(5π/6) = -√3/2.