Find the exact value of the expression sin945 degree by goin

Find the exact value of the expression sin(-945 degree) by going through steps. Find a coterminal angle. Find the reference angle. Find the exact value of the expression sin(-945 degree) by using the reference angle (determine the correct sign).

Solution

a) coterminal angle of sin (-945)

coterminal angles are angles in standard position

to find co terminal angle add/ subtract 360 degrees from the angle

so angle coterminal with -945 degrees is 3*360 - 945 = 135 degrees

b) reference angle = 45 degrees ( in 2nd quadrant )

c) therefore, exact value of sin ( -945) = sin ( 45) = 1/ sqrt 2 = sqrt 2 / 2