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The sine of the measure of an angle in a right triangle, is the ratio of the opposite side of that angle, to the hypotenuse.

The cosine of the measure of an angle in a right triangle, is the ratio of the adjacent side of that angle, to the hypotenuse.


According to these, we have:

[tex]\displaystyle{ \sin(x^{\circ})= \frac{6}{10} [/tex]

and


[tex]\displaystyle{ \sin(y^{\circ})= \frac{6}{10} [/tex].


Thus, the ratios of both are identical [tex]( \frac{6}{10} \ and \ \frac{6}{10} )[/tex]


The ratios of sin (x) and cos (y) are both identical  [tex](\frac{6}{10}\; and\; \frac{6}{10})[/tex].

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  A math tool applied for finding angles or sides in a right triangle is trigonometric ratios.

The main trigonometric ratios are:

[tex]sin(\alpha )=\frac{opposite\;side}{hypotenuse} \\ \\ cos(\alpha )=\frac{adjacent\;side}{hypotenuse}\\ \\ tan(\alpha )=\frac{sin (\alpha )}{cos(\alpha } =\frac{opposite\;side}{adjacent\;side}[/tex]

The question asks the sin x and cos y, for solving this you should apply the trigonometric ratios. Therefore,

[tex]sin (x)=\frac{opposite\; side}{hypotenuse} =\frac{6}{10}[/tex]

and

[tex]cos (y)=\frac{adjacent\; side}{hypotenuse} =\frac{6}{10}[/tex]

Learn more about trigonometric ratios here:

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