In quadrant III, the cosine function is negative.
Since sinθ = -5/2, and sinθ = opposite/hypotenuse, we can assign the opposite side to be -5 and the hypotenuse to be 2.
Using Pythagorean theorem, we can find the adjacent side:
a² + (-5)² = 2²
a² + 25 = 4
a² = 4 - 25
a² = -21
Since we are in quadrant III, the cosine function is negative, so we take the negative square root:
a = -√(-21)
Thus, the value of cosineθ is -√(-21), or, in simplest form:
cosθ = -√21
Given sine, theta, equals, minus, start fraction, 2, divided by, 5, end fractionsinθ=− 5 2 and angle thetaθ is in Quadrant III, what is the exact value of cosine, thetacosθ in simplest form? Simplify all radicals if needed.
1 answer