Find exact value

Question

Cos theata=12/15 , tan theata<0

Answer 1

cos(theta) = 12/15

theta in either quadrant I or IV

sin(theta) = 9/15 or -9/15

theta in quadrant I or II if sin(theta) >0

if sin(theta) <0 then theta is in quadrant III or IV

theta is in quadrant IV

tan(theta) = sin(theta))/cos(theta) = -9/15/12/15 = -9/12 = -3/4= -0.75 <0

theta = about -36.87 degrees or 360-36.87 = 323.13 degrees + 360n where n = any integer

theta is in quadrant IV