Given sine, theta, equals, one quartersinθ=

Question

4
1
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and angle thetaθ is in Quadrant I, 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=

Answer 1

To find the exact value of cosine theta (cosθ), we can use the Pythagorean identity:

sin^2θ + cos^2θ = 1

Since we are given sinθ = 1/4, we can square it to find sin^2θ:

(1/4)^2 = 1/16

Now we can substitute the value of sin^2θ into the Pythagorean identity:

1/16 + cos^2θ = 1

To isolate cos^2θ, we can subtract 1/16 from both sides:

cos^2θ = 1 - 1/16
cos^2θ = 16/16 - 1/16
cos^2θ = 15/16

Now we can take the square root of both sides to find the value of cosθ:

cosθ = ±√(15/16)

Since the angle theta is in Quadrant I, cosine theta will be positive:

cosθ = √(15/16)

Simplifying the radical by canceling out the perfect square:

cosθ = √15/√16

Finally, we can simplify the radical further:

cosθ = (√15)/(√16)
cosθ = (√15)/4

Therefore, the exact value of cosine theta (cosθ) is (√15)/4.