Evaluate the following expressions Your answer must be an ex

Evaluate the following expressions. Your answer must be an exact angle in radians.

a.sin^-1(-1/2)

b.arccos(-1/2)

Solution

By using trignometric identities we know that

sin^-1 (-x)=-sin^-1 (x)

Sin^-1 (-1/2)= - sin^-1 (1/2)= - pi/6 radians or -30 degree

b)cos^-1(-x)=pi-cos^-1 (x)

Cos^-1 (-1/2)= pi-cos^-1 (1/2)=pi-pi/3=2pi/3 radians or

120 degree