Evaluate by using the Pythagorean identities

Question

Find sin θ and cos θ if tan θ=1/6 and sin θ >0

Answer 1

tan = sin / cos ... cos = 6 sin

sin^2 + cos^2 = 1 ... 37 sin^2 = 1

Answer 2

tanθ and sinθ are both positive only in QI

Draw your standard triangle. You have
y = 1
x = 6
r = √37

tanθ = y/x
sinθ = y/r
cosθ = x/r