Use trigonometric identities to find the exact values of sinθ and tanθ given that cosθ =1/6 and 3pi/2 ≤ θ ≤ 2pi. Answer should not include decimals.

Answer 1

Since θ lies in the fourth kwadrant (3π/2 < θ < 2π) we know that:

sin(θ) < 0

tan(θ) < 0

By definition:

tan(θ) = sin(θ)/cos(θ) = 6 sin(θ)

Pythagorean identity:

sin²(θ) + cos²(θ) = 1

sin(θ) = ± √(1-cos²(θ)) with the negative one the correct one.

sin(θ) = - √(35)/6

tan(θ) = -√(35)

Answer 2

sine² + cosine² = 1

tangent = sine / cosine