Summary

• Radian measure is defined such that the angle associated with the arc of length 1 on the unit circle has radian measure 1

• For acute angles $\theta$, the values of the trigonometric functions are defined as rations 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 are periodic

  • $\sin$, $\cos$, $\sec$, $\csc$ functions have a period of $2\pi$
  • $\tan$ and $\cot$ functions have period $\pi$

  

  

  

Radian Measure

Angle of $360\degree$ is the circumference of a circle, an arc length of $2\pi$

Six Basic Trigonometric Functions

Let $P = (x, y)$ be a point on the unit circle cnetered at the origin $O$, let $\theta$ be an angle with an intial side along the positive x-axis and a terminal side given the line segment $OP$, defining the trigonometric functions as:

If x = 0, $\sec\theta$ and $\tan\theta$ are undefined, if y = 0, $\cot\theta$ and $\csc\theta$ are undefined

Even and Odd Functions

• Function is even if $f(-x) = f(x)$ for all $x$ in the domain of $f$
• Function is odd if $f(-x) = -f(x)$ for all $x$ in the domain of $f$

Special Triangles

Trigonometric Identities

Graphs and Periods of Trigonometric Functions