Use the Pythagorean Identity first and then the Tangent Identity to find tanθ if cosθ=-1/2 and θ terminates in Quadrant II. (3 points)

Question

Hint: Find sin θ as you did in problem #1. Continue by using the Tangent Identity.

Answer 1

Using the Pythagorean Identity:
sin^2θ + cos^2θ = 1
sin^2θ + (-1/2)^2 = 1
sin^2θ + 1/4 = 1
sin^2θ = 3/4
sinθ = ±√(3)/2
Since θ terminates in Quadrant II, sinθ is positive.

Using the Tangent Identity:
tanθ = sinθ/cosθ
tanθ = (√(3)/2) / (-1/2)
tanθ = -√(3)

Therefore, tanθ = -√(3).