If cos theta 513 and sin theta 0 find tan theta Solutionas

If cos theta = 5/13 and sin theta > 0. find tan theta,

Solution

as cos is -ve and sin is +ve then theta must be in 2nd quadrant, so tan(theta) must be -ve.

tan(theta) = sin(theta)/cos(theta) = sqrt(1 - cos²(theta))/cos(theta)

= sqrt(1- 25/169)/(-5/13)

= -12/5 = -2.4