Given cosine, theta, equals, start fraction, square root of, 33, end square root, divided by, 7, end fractioncosθ=
7
33
and angle thetaθ is in Quadrant I, what is the exact value of sine, thetasinθ in simplest form? Simplify all radicals if needed.
In Quadrant I, both cosine and sine are positive.
Since cosine is the adjacent side divided by the hypotenuse, we can form a right triangle with the adjacent side as 7 and the hypotenuse as √33.
Using the Pythagorean theorem, we can find the value of the opposite side (sine):
opposite side^2 + adjacent side^2 = hypotenuse^2
opposite side^2 + 7^2 = (√33)^2
opposite side^2 + 49 = 33
opposite side^2 = 33 - 49
opposite side^2 = -16
Since the side lengths of a right triangle cannot be negative, there is no corresponding value for sineθ in this case.