In previous lessons, we recalled that any right triangle with acute angles of 25 and 65 degrees was similar to any other right triangle with these same acute angles. Revisiting these triangles, we notice that the sine of 25 degrees is equal to the cosine of 65 degrees, and the cosine of 25 degrees is equal to the sine of 65 degrees.

Mathematicians often use Greek letters to represent angles. For instance, is a Greek letter we use frequently in trigonometry. Looking at a general right triangle, the angles can be written as 90, , and . Using this general right triangle, we can fill out the table again. Notice that the same fraction, , appears for both and . That’s how we know for any acute angle .