Question

The angle θ lies in Quadrant II.

sinθ=34

What is cosθ?



Responses

7√4
fraction numerator square root of 7 end numerator over denominator 4 end fraction

34
three fourths

−34
negative three fourths

−7√4

Answer 1

First note: sinθ = 34 as written is impossible (|sinθ| ≤ 1). I assume you mean sinθ = 3/4.

Since θ is in Quadrant II, cosine is negative. Use sin^2θ + cos^2θ = 1:

cosθ = −√(1 − sin^2θ) = −√(1 − (3/4)^2) = −√(1 − 9/16) = −√(7/16) = −√7 / 4.

Answer: −√7/4.