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

−2√3
negative Start Fraction Start Root 2 End Root over 3 End Fraction

42√9

Answer 1

sin²θ = (7/9)² = 49/81.
cos²θ = 1 − sin²θ = 1 − 49/81 = 32/81, so cosθ = ±√(32/81) = ±(4√2)/9.
Since π/2 < θ < π (second quadrant), cosθ < 0.
Thus cosθ = −(4√2)/9.