## If the cos of an angle is .75, what is the csc? A. 1/√(5) B. 9/√(6) C. 6/√(2) D. 3/√(9) E. 4/√(7) F. 2/√

Question

If the cos of an angle is .75, what is the csc?
A. 1/√(5)
B. 9/√(6)
C. 6/√(2)
D. 3/√(9)
E. 4/√(7)
F. 2/√(3)

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1 year 2021-08-14T15:01:32+00:00 1 Answers 13 views 0

This is the same as writing $$\frac{4}{\sqrt{7}}$$

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Explanation:

0.75 = 3/4

Recall that cosine is the ratio of adjacent over hypotenuse.

That means if cos(theta) = 3/4, then the adjacent is 3 units and the hypotenuse is 4 units.

Through the pythagorean theorem, we would then find that

a^2+b^2 = c^2

a = sqrt(c^2 – b^2)

a = sqrt(4^2 – 3^2)

a = sqrt(7)

This is the opposite side of reference angle theta.

From here, we can say

csc(angle) = hypotenuse/opposite

csc(theta) = 4/sqrt(7)

which points to choice E as the final answer.