Why are the values for sine and cosine equal at 45°?

For this case we have a rectangle triangle.

The opposite leg is the sine of the angle.

The adjacent catheto is the cosine of the angle.

For 45 degrees, the length of both legs is the same.

Thus,

Sine (45) = Cosine (45)

Answer:

The length of the legs is the same for a 45 degree angle.