We have to calculate the sin of x and cos of y.
We can write the sine of an angle as the ratio between the opposite side and the hypotenuse of the right triangle.
For the cosine of an angle, the ratio is between the adyacent side and the hypotenuse.
So the sine of x can be written as:
[tex]\sin (x)=\frac{Opposite}{Hypotenuse}=\frac{8}{OP}=\frac{8}{\sqrt[]{8^2+15^2}}=\frac{8}{17}[/tex]
For the cosine of y we have:
[tex]\cos (y)=\frac{Adyacent}{Hypotenuse}=\frac{8}{OP}=\frac{8}{17}[/tex]
As the adyacent of y is the same side that is the opposite to x, we have that:
[tex]\sin (x)=\cos (y)[/tex]
The ratios also share the hypotenuse in the denominator.
Answer:
sin(x) = cos(y) = 8/17
The ratios share the numerator (the adyacent side of y is the same side that is opposite to x) and the denominator (the hypotenuse).
