Question

Given sin0= 3/7, and tan0 <0, what is the value of coso?

Answer 1

sin θ = 3 / 7 = .429

sin^2 θ + cos^2 θ = 1      trig identity

9/49 + cos^2 θ = 1

cos^2 θ = 40 / 49 = .816       cos θ = .903

Check .429^2 + .903^2 = 1

cos .903 = 25.4 deg

In the second quadrant sin = +, cos = -, tan = -

So 25.4 deg in the second quadrant = 180 - 25.4 = 154.6 deg

Check:

sin 154.6 = .428

cos 154.6 = -.903

tan 154.6 = -.475