Question

Find the cosine for an angle that has a sine of 340√20
and is in Quadrant II. Use the Pythagorean identity sin2θ+cos2θ=1
and the quadrant to solve.(1 point)
Responses

110

Start Fraction 1 over 10 End Fraction

10√10

Start Fraction Start Root 10 End Root over 10 End Fraction

−10√10

negative Start Fraction start root 10 end root over 10 End Fraction

−110

Answer 1

cos^2θ = 1 − sin^2θ = 1 − (3√10/10)^2 = 1 − 90/100 = 1/10, so cosθ = ±√(1/10) = ±√10/10.
In Quadrant II cosine is negative, so cosθ = −√10/10.