Solve the following If costheta 817 what are the two possib

Solve the following. If cos(theta) = -8/17, what are the two possible values of sin(theta)? (Enter your answers as a comma-separated list.) If sin(theta) = 0.8 and theta is in the third quadrant of the xy plane, what is cos(theta)? If sin(theta) = -3/4, what is sin(pi/2 - theta)? (Enter your answers as a comma-separated list.)

Solution

cos theta=8/17

here cos theta is positive and cos theta is positive in first and fourth quadrant

adjacent=8   and hypotenuse=17

opposite=sqrt(289-64)=15

If theta is in first quadrant

sin theta=15/17

and if theta is in last quadrant

sin theta=-15/17

So the two possible solutions are

15/17,-15/17