Question

Use the triangle to answer the question.

Answer 1

Answer: Choice D) sin(x)/cos(y) = 1

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Label the sides as shown in the image attachment. 

P = horizontal leg (opposite of angle x; adajcent to angle y)
Q = vertical leg (opposite of angle y; adajcent to angle x)
R = hypotenuse (longest side; always opposite the 90 degree angle)

Use the definitions of sine and cosine to say...

sin(Angle) = opposite/hypotenuse
sin(x) = P/R

and

cos(angle) = adjacent/hypotenuse
cos(y) = P/R

Notice how sin(x) = cos(y). This is true any time x+y = 90 which is the case here (x and y are complementary angles). A more specific example is sin(30) = cos(60) which are both equal to 1/2 or 0.5

Since sin(x) = cos(y), this means sin(x)/cos(y) = 1 as any expression divided by itself is equal to 1. Keep in mind that cos(y) cannot equal zero.

This is why choice D is the final answer.

side note: something like cos(x)/sin(y) or sin(y)/cos(x) or similar are all equal to 1 as long as x+y = 90