If sin theta 23 tan theta 0 find sec theta please show work

If sin theta =2/3, tan theta < 0,   find sec theta         please show work

Solution

sin theta =2/3, tan theta < 0,   find sec theta

now we have : tan theta < 0 , sin theta>0 ---> theta is in IInd quadrant

base = sqrt( 3^2 -2^2) = sqrt5

costheta = -sqrt5/3

sectheta =1/costheta = -3/sqrt5