Given sine, theta, equals, minus, start fraction, 4, divided by, 7, end fractionsinθ=−
7
4
and angle thetaθ is in Quadrant IV, what is the exact value of cosine, thetacosθ in simplest form? Simplify all radicals if needed.
Answer
Attempt 2 out of 2
cosine, theta, equalscosθ=
Since sine is negative in Quadrant IV, cosine will be positive. Therefore,
cosθ = √(1 - sin^2θ)
cosθ = √(1 - (-7/4)^2)
cosθ = √(1 - 49/16)
cosθ = √(16/16 - 49/16)
cosθ = √(-33/16)
Since the square root of a negative number is not a real number, the exact value of cosθ is undefined in this case.