Question
using the Pythagorean Identity to find the exact value (i.e. Radicals and fractions, not rounded decimals) of sin θ if cosθ=1/2 and θ terminates in Quadrant IV. (2 points)
Answers
Answered by
GPT 3.5
Since cosθ=1/2 in Quadrant IV, sinθ will be negative.
The Pythagorean Identity is sin^2θ + cos^2θ = 1.
Substitute cosθ=1/2 into the identity: sin^2θ + (1/2)^2 = 1
sin^2θ + 1/4 = 1
sin^2θ = 3/4
sinθ = -√3/2
Therefore, sinθ = -√3/2.
The Pythagorean Identity is sin^2θ + cos^2θ = 1.
Substitute cosθ=1/2 into the identity: sin^2θ + (1/2)^2 = 1
sin^2θ + 1/4 = 1
sin^2θ = 3/4
sinθ = -√3/2
Therefore, sinθ = -√3/2.