cos is [tex]\frac{adjacent}{hypotenuse}[/tex]. So, if cos(a)= [tex]\frac{5}{13}[/tex] then use Pythagorean Theorem to determine the length of the "opposite" side.
5² + x² = 13²
25 + x² = 169
x² = 144
x = 12
Now that you know the length of the opposite side, you can plug it in for sin.
sin is [tex]\frac{opposite}{hypotenuse}[/tex]. So, sin(a) = [tex]\frac{12}{13}[/tex]
Now, if you switch so you are looking for sin(b), the cos and sin also switch.
cos(b) = sin(a) = [tex]\frac{12}{13}[/tex]
sin(b) = cos(a) = [tex]\frac{5}{13}[/tex]
Answer: sin(b) = [tex]\frac{5}{13}[/tex]
