AP Precalculus Unit 3: Periodic Phenomena

θ=s/r, where θ is the angle in radians, s is the arc length, and r is the radius.

A complete turn around the circle is equal to 2π radians.

Angles that share the same initial and terminal sides, but differ in the amount of rotation.

The sides are in the proportion 1:1:√2, where √2 is the hypotenuse.

The range is [-1, 1], meaning sine and cosine values always fall between -1 and 1, inclusive.

Special triangles on the unit circle help in determining exact trigonometric ratios for common angles.

Phenomena that repeat their pattern over time or space.

The period is the horizontal length of one complete cycle of the function.

An interval of increase is an range of x-values where the function's value increases from left to right.

Concavity describes how a curve bends; it's concave up if it 'holds water', concave down if it 'spills water'.

An angle in standard position has its vertex at the origin and its initial side along the positive x-axis.

The change in the function's output divided by the change in its input; rise over run.