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

−117√

negative Start Fraction 1 over Start Root 17 End Root 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
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Answer 1

cos θ = −√33/17

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