Unit Circle and Trig Identities (Introduction)

The unit circle has radius 1 centered at the origin. A point at angle theta has coordinates (costheta, sintheta). Key angles (memorize!): | theta | costheta | sintheta | |---|---|---| | 0° | 1 | 0 | | 30° | frac{sqrt{3}}{2} | frac{1}{2} | | 45° | frac{sqrt{2}}{2} | frac{sqrt{2}}{2} | | 60° | frac{1}{2} | frac{sqrt{3}}{2} | | 90° | 0 | 1 | | 180° | -1 | 0 | | 270° | 0 | -1 | | 360° | 1 | 0 | In…

Example: Find sin(150°) and cos(150°).

Pythagorean: sin^2theta + cos^2theta = 1 Reciprocal: - sectheta = frac{1}{costheta} - csctheta = frac{1}{sintheta} - cottheta = frac{1}{tantheta} = frac{costheta}{sintheta} Quotient: tantheta = frac{sintheta}{costheta}