Question

Find the exact value of sin theta, if cos theta = 1/5 and tan theta < 0

Answer 1

cos theta = 1/5 and tan theta < 0

cos positive and tan theta negative are in fourth quadrant,

Thus, theta is in fourth quadrant,

In fourth quadrant, sin theta is negative.

cos theta = adj/hyo=1/5

adj=1 and hyp =5

Calculate the opp.

opp = sqrt(hyp^2 - adj^2)

       =sqrt(5^2 -1^2)

      =sqrt(24)

      =2sqrt(6)

Calculate the sin theta.

sin theta = opp/hyp =2sqrt(6)/5

In fourth quadrant, sin theta is negative.

sin theta  = - 2sqrt(6)/5