Given the triangle below
From the triangle above, we can find the value of the longest side, hypothenus (OP) using the pythagoras theorem as shown below:
[tex]\begin{gathered} OP^2=4^2+3^2 \\ OP^2=16+9 \\ OP^2=25 \\ OP=\sqrt[]{25} \\ OP=5 \end{gathered}[/tex]
Since we know all the sides of the triangle, it will be easy to find sin x and cos y
With reference to angle x°, the opposite side is 3, the adjacent side is 4, and the longest side, hypothenuse is OP= 5, therefore;
[tex]\begin{gathered} \sin x^0=\frac{opposite}{\text{hypothenuse}} \\ \sin x^0=\frac{3}{5} \end{gathered}[/tex]
With reference to the angle y°, the opposite is 4, the adjacent is 3, and the longest side, hypothenuse OP is 5, therefore:
[tex]\begin{gathered} \cos y^0=\frac{adjacent}{hypothenuse} \\ \cos y^0=\frac{3}{5} \end{gathered}[/tex]
The ratio of sin x and cos y is
[tex]\begin{gathered} \sin x^0\colon\cos y^0 \\ \frac{3}{5}\colon\frac{3}{5} \\ 1\colon1 \end{gathered}[/tex]
Hence, the relationship the ratios of sin xº and cos yº shared is the same or identical, or simply 1:1
