For angle 0, cos0=5/13. What is the value of sin0cos0?

Notice that  "y"  might take on two values here...  ±12  ...depending upon the quadrant in which the angle lies........

So........

sinΘ cosΘ  = ( ±12 / 13 ) (5 / 13) =  ±60 / 169

If cos(θ) = 5/13, then you can have a right triangle with the adjacent side = 5 and hypotenuse = 13.

Using the Pythagorean Theorm, the opposite side = 12. This makes sin(θ) = 12/13.