The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. In the table … See more

A trigonometric number is a number that can be expressed as the sine or cosine of a rational multiple of π radians. Since See more

As discussed in § Constructibility, only certain angles that are rational multiples of $${\displaystyle \pi }$$ radians have trigonometric values that can be expressed with square roots. The angle 1°, being
Using the triple … See more

• Lehmer, D. H. (1933). "A note on trigonometric algebraic numbers". American Mathematical Monthly. 40 (3): 165–166. See more

45°
From a reflection identity, $${\displaystyle \cos(45^{\circ })=\sin(90^{\circ }-45^{\circ })=\sin(45^{\circ })}$$. Substituting into the Pythagorean trigonometric identity
A geometric way of deriving the sine or cosine of 45° is by … See more

• Ailles rectangle, used to find exact values for multiples of 15°
• List of trigonometric identities See more