In Quadrant III, the sine function is negative. We can use the Pythagorean Identity to find the value of sine theta.
Since cosine theta is equal to -(√21)/5, we can let the adjacent side be -(√21) and the hypotenuse be 5. By the Pythagorean Theorem, we can find the opposite side.
Let the opposite side be x.
(√21)^2 + x^2 = 5^2
21 + x^2 = 25
x^2 = 4
x = 2
So, the exact value of sine theta, sin(theta), is -2/5.
Given cosine, theta, equals, minus, start fraction, square root of, 21, end square root, divided by, 5, end fractioncosθ=−
5
21
and angle thetaθ is in Quadrant III, what is the exact value of sine, thetasinθ in simplest form? Simplify all radicals if needed.
1 answer
1 answer