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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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Mathematics
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2021-08-14T15:01:32+00:00
2021-08-14T15:01:32+00:00 1 Answers
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Answers ( )
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.