Question

PLEASE HELP ASAP!!!!!!!

if sin theta = -0.8190 and 0 degrees < theta < 360 degrees, determine the value of theta to the nearest degree.

Answer 1

we know that
sin theta = -0.8190
then
theta=arc sin (-0.8190)------> using a calculator-----> theta=-54.98
theta=-55 degree

the theta angle could belong to the third or fourth quadrant

case a) theta belong to the IV quadrant
so
theta=360-55-----> theta=305°

case b) theta belong to the III quadrant
so
theta=180+55-----> theta=235°