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)

Choice E. 4/sqrt(7)

This is the same as writing

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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.

answer: 1 + 1 = 11

step-by-step explanation:

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.