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Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?


A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 12, another leg across from angle x measuring 5, and the hypotenuse measuring 13.


The ratios are opposites (negative five thirteenths and five thirteenths).

The ratios are both identical (five thirteenths and five thirteenths).

The ratios are reciprocals (five thirteenths and thirteen fifths).

The ratios are both negative (negative thirteen fifths and negative thirteen fifths).

Use The Image Below To Answer The Following Question What Relationship Do The Ratios Of Sin X And Cos Y ShareA Right Triangle Is Shown The Two Angles That Are N class=

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Answer:

  (b)  The ratios are both identical (five thirteenths and five thirteenths).

Step-by-step explanation:

The mnemonic SOH CAH TOA can remind you of the relationships between trig functions and sides of a right triangle. In this problem, we're interested in ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

If we name the right angle vertex Q, then these tell you that ...

  sin(x°) = OQ/OP = 5/13

  cos(y°) = OQ/OP = 5/13

The sin(x°) and cos(y°) ratios are identical. Both are 5/13.

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Additional comment

You may have noticed that the side opposite one of the acute angles in right triangle is the side that is adjacent to the other acute angle. That means the sine of an angle is always equal to the cosine of its complement.

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