ABSTRACT
Content Students are led through a paper-folding method to prove the double-angle formulas for sin x and cos x. A different folding of 45◦-45◦-90◦ and 30◦-60◦-90◦ triangles is used to discover exact expressions for the side lengths of a 15◦-75◦-90◦ triangle and a 22.5◦-67.5◦-90◦ triangle, respectively. From this, exact expressions for sine, cosine, and tangent can be found for 15◦, 75◦, 22.5◦, and 67.5◦ angles.
