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

Answers ( )

  1. minhkhang
    0
    2021-08-14T15:02:59+00:00
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    Answer: Choice E. 4/sqrt(7)

    This is the same as writing [tex]\frac{4}{\sqrt{7}}[/tex]

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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.

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