Essential Concepts

• Radian measure is defined such that the angle associated with the arc of length 1 on the unit circle has radian measure 1. An angle with a degree measure of 180° has a radian measure of $\pi$ rad.
• For acute angles $\theta$, the values of the trigonometric functions are defined as ratios of two sides of a right triangle in which one of the acute angles is $\theta$.
• For a general angle $\theta$, let $(x,y)$ be a point on a circle of radius $r$ corresponding to this angle $\theta$. The trigonometric functions can be written as ratios involving $x, \, y$, and $r$.
• The trigonometric functions are periodic. The sine, cosine, secant, and cosecant functions have period $2\pi$. The tangent and cotangent functions have period $\pi$.