Question

Given sin\theta =-(\sqrt(21))/(5) and angle \theta is in Quadrant III, what is the exact value of cos\theta in simplest form? Simplify all radicals if needed.

Answer 1

The exact value of cos(theta) is 2/5.

Step-by-step explanation:

To find the value of cos(theta), we can use the Pythagorean identity that relates the sine and cosine of an angle:

sin^2(theta) + cos^2(theta) = 1

Given that sin(theta) = -sqrt(21)/5, we can square this value:

sin^2(theta) = (sqrt(21)/5)^2 = 21/25

Plugging this into the Pythagorean identity, we have:

21/25 + cos^2(theta) = 1

Simplifying, we find:

cos^2(theta) = 4/25

Taking the square root of both sides, we get:

cos(theta) = sqrt(4/25) = 2/5