Given cosine, theta, equals, minus, start fraction, square root of, 35, end square root, divided by, 6, end fractioncosθ=−

Question

6
35
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and angle thetaθ is in Quadrant II, what is the exact value of sine, thetasinθ in simplest form? Simplify all radicals if needed.

Answer 1

To find the exact value of sine theta, we can use the Pythagorean identity.

The Pythagorean identity states that for any angle theta, sin^2(theta) + cos^2(theta) = 1.

Since we are given cos(theta) = -sqrt(35)/6, we can square it to find sin^2(theta).

(sin^2(theta) )+ (cos^2(theta)) = 1

sin^2(theta) + (-sqrt(35)/6)^2 = 1

sin^2(theta) + 35/36 = 1

sin^2(theta) = 1 - 35/36

sin^2(theta) = (36/36) - (35/36)

sin^2(theta) = 1/36

Taking the square root of both sides, we get:

sin(theta) = sqrt(1/36)

sin(theta) = 1/6

Therefore, the exact value of sin(theta) is 1/6.