Question

Find the exact value of CSC Theta for an angle Theta with cosine Theta with equals -2/5 and with its terminal side in quadrant 2

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Answer 1

A

Explanation:

Cos(theta) = -2/5

From sin^2(theta) + cos^2(theta) = 1 we get

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

sin(theta) = sqrt(1 - cos^2(theta)). The root is the positive one in quad 2

sin(theta) = sqrt(1 - cos^2(theta))

sin(theta) = sqrt(1 - (-2/5)^2)

sin(theta) = sqrt(1 - 4/25)

sin(theta) = sqrt(21/25)

sin(theta) = sqrt(21)/5

csc(theta) = 1/sin(theta)

csc(theta) = 1/sqrt(21)/5

csc(theta) = 5/sqrt(21)

The answer should be the denominator rationalized as in

csc(theta) = 5 * sqrt(21) / 21.

However that is not an option, so the answer is A