How can I determine the exact values for the sine, cosine, and tangent of a 45-degree angle?

To determine the exact values for sine, cosine, and tangent of a 45-degree angle, consider a right triangle with equal legs. The hypotenuse is √2 times the leg length. Thus, sin(45°) = cos(45°) = 1/√2 or √2/2, and tan(45°) = 1.