Question

If sin y° = 9 divided by c. and tan y° = 9 divided by d. ,what is the value of cos y°?

Answer 1

Answer: The fraction d/c

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Explanation:

Check out the attached image. I've labeled the three sides of the triangle based on the reference angle y. The opposite side is 9, the adjacent is d, and the hypotenuse is c.

How did I get those values? Well

sine = opposite/hypotenuse = 9/c

tangent = opposite/adjacent = 9/d

matching terms we see that opposite = 9, adjacent = d, hypotenuse = c

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Now we compute the ratio for cosine

cosine = adjacent/hypotenuse

cos(y) = d/c

We don't have enough info to know the numeric value of d/c

Answer 2

$\bf sin(y)=\cfrac{\stackrel{opposite}{9}}{\stackrel{hypotenuse}{c}}\qquad \qquad \qquad tan(y)=\cfrac{\stackrel{opposite}{9}}{\stackrel{adjacent}{d}} \\\\\\ cos(y)=\cfrac{\stackrel{adjacent}{d}}{\stackrel{hypotenuse}{c}}$