If cosθ=1/4 and θ is in Quadrant I, find sinθ .(1 point)
Since θ is in Quadrant I and the cosine of θ is positive, we know that the sine of θ is also positive.
Using the Pythagorean identity, we have:
sin^2θ + cos^2θ = 1
Plugging in the given value for cosine, we can solve for sine:
sin^2θ + (1/4)^2 = 1
sin^2θ + 1/16 = 1
sin^2θ = 1 - 1/16
sin^2θ = 15/16
Taking the square root of both sides, we get:
sinθ = √(15/16)
Since sinθ is positive and θ is in Quadrant I, we can write:
sinθ = √(15/16)
So, sinθ = √15/4 ≈ 0.97.