Question

Ana was asked to use triangles formed by angles on the unit circle to prove the Pythagorean Identity sin2θ+cos2θ=1
, where sinθ=1617
and π2<θ<π
. What value should she use for cosθ
?(1 point)
Responses

33√17

Start Fraction Start Root 33 End Root over 17 End Fraction

−33√17

negative Start Fraction Start Root 33 End Root over 17 End Fraction

117√

Start Fraction 1 over Start Root 17 End Root End Fraction

−117√

Answer 1

cos θ = −√33 / 17

Reason: cos^2θ = 1 − sin^2θ = 1 − (16/17)^2 = 33/289, so cosθ = ±√(33)/17. Since π/2 < θ < π (quadrant II), cosine is negative.