Use an appropriate addition formula to simplify the expressi

Use an appropriate addition formula to simplify the expression sin (theta + 3 pi/2).

Solution

sin ( theta + 3pi/2 )

applying sin ( a+ b ) formula

sin (a+b) = sin a cos b + cos a sin b

sin ( theta + 3pi/2 ) = sin theta cos 3pi/2 + cos theta sin 3pi/2

cos 3 pi/2 = 0

sin 3pi/2 = -1

= 0 + cos theta (-1)

= - cos theta