Given sine, theta, equals, minus, start fraction, square root of, 11, end square root, divided by, 6, end fractionsinθ=−
6
11
and angle thetaθ is in Quadrant III, what is the exact value of cosine, thetacosθ in simplest form? Simplify all radicals if needed.
Answer
Attempt 1 out of 2
cosine, theta, equalscosθ=
The cosine of an angle in Quadrant III is negative. Since the sine of θ is −√11/6, we can use the Pythagorean identity to find the cosine:
cosθ = -√(1 - sin²θ)
= -√(1 - (-√11/6)²)
= -√(1 - 11/36)
= -√(25/36)
= -√25/√36
= -5/6
Therefore, the exact value of cosine θ is -5/6.