Question

Using the Pythagorean Identity, determine cosθ
if sinθ=79
and π2<θ<π
.(1 point)
Responses

−42√9

negative Start Fraction 4 Start Root 2 End Root over 9 End Fraction

42√9

Start Fraction 4 Start Root 2 End Root over 9 End Fraction

2√3

Start Fraction Start Root 2 End Root over 3 End Fraction

−2√3

Answer 1

sin^2θ + cos^2θ = 1. With sinθ = 7/9:

cos^2θ = 1 − (7/9)^2 = 1 − 49/81 = 32/81, so cosθ = ±(√32)/9 = ±(4√2)/9.

Since π/2 < θ < π (second quadrant) cosine is negative, so cosθ = −4√2/9.