How do i find the sin 11pi/2 without using a calculator?

The values of sin cycle on the domain 0 to 2π

The value of sin (π/2) = 1

The value of sin (2π/2) = 0

The value of sin (3π/2) = sin (π + π/2) = - 1

Therefore, if the angle can be written as:

nπ + π/2, where n is any odd number, the value of sin (nπ + π/2) = - 1

sin (11π/2) = sin (5π + π/2) = - 1