complementaryFor any given right-angled triangle, the Pythagoras theorem states that
[tex](hypothenuse)^2=(opposite)^2+(adjacent)^2[/tex]
Also, the trigonometric ratios are given as
[tex]\begin{gathered} \sin =\frac{\text{opposite}}{\text{hypothenuse}} \\ \cos =\frac{\text{adjacent}}{\text{hypothenuse}} \\ \tan =\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]
From the right-angled triangle given in the question
[tex]\begin{gathered} OP^2=15^2+8^2 \\ OP^2=225+64 \\ OP^2=289 \\ OP=\sqrt[]{289} \\ OP=17 \end{gathered}[/tex][tex]\begin{gathered} \sin x=\frac{8}{17} \\ \cos y=\frac{8}{17} \end{gathered}[/tex]
The ratio of sin x and cos y will give
[tex]\frac{\sin x}{\cos y}=\frac{\frac{8}{17}}{\frac{8}{17}}=1[/tex]
The relationship between sin x and cos y share is 1 which is because x and y are complimentary angles
Hence, sin x= 8/17, cos y= 8/17, and the ratio of sin x and cos y is 1
