What is cos(2arcsin(-1/2))?

1 Answer
Jan 2, 2016

1/2

Explanation:

cos(2arcsin(-1/2))

The range of arcsin(x) is [-pi/2, pi/2]

Ask the question which angle in [-pi/2, pi/2] gives sin(x)=-1/2

sin(x)=-1/2 then x = -pi/6#

Our problem now becomes

cos(2(-pi/6))
=cos(-pi/3)
=cos(pi/3) = 1/2 Answer