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 [latex]\pi [/latex] rad.
- For acute angles [latex]\theta[/latex], 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 [latex]\theta[/latex].
- For a general angle [latex]\theta[/latex], let [latex](x,y)[/latex] be a point on a circle of radius [latex]r[/latex] corresponding to this angle [latex]\theta[/latex]. The trigonometric functions can be written as ratios involving [latex]x, \, y[/latex], and [latex]r[/latex].
- The trigonometric functions are periodic. The sine, cosine, secant, and cosecant functions have period [latex]2\pi[/latex]. The tangent and cotangent functions have period [latex]\pi[/latex].
Key Equations
- Generalized sine function
[latex]f(x)=A\sin(B(x-\alpha))+C[/latex]
Glossary
- periodic function
- a function is periodic if it has a repeating pattern as the values of [latex]x[/latex] move from left to right
- radians
- for a circular arc of length [latex]s[/latex] on a circle of radius 1, the radian measure of the associated angle [latex]\theta [/latex] is [latex]s[/latex]
- trigonometric functions
- functions of an angle defined as ratios of the lengths of the sides of a right triangle
- trigonometric identity
- an equation involving trigonometric functions that is true for all angles [latex]\theta [/latex] for which the functions in the equation are defined
