CCSSAPhigh school
AP Precalculus — Periodic Functions
Trigonometric foundations, sinusoidal graphing, periodic modeling, and polar/parametric representations. Covers AP Precalculus Unit 3 content: unit circle, sine/cosine parameters, transformations of periodic functions, real-world sinusoidal models, polar coordinates, and parametric equations.
4units
6topics
99questions
~2hours
Course Units
Learning objectives
- Define sine and cosine using the unit circle (x-coordinate, y-coordinate)
- Convert between degree and radian measure
- Evaluate exact trig values at standard angles (0, pi/6, pi/4, pi/3, pi/2)
- Identify the domain, range, and period of parent sine and cosine functions
Topics in this unit
Learning objectives
- Extract amplitude, period, phase shift, and midline from y = A sin(Bx + C) + D
- Distinguish inside parameters (B, C) from outside parameters (A, D)
- Graph sinusoidal functions by applying transformations in correct order
- Determine max, min, and range from amplitude and midline
- Construct a sinusoidal equation from a set of given constraints
Topics in this unit
Learning objectives
- Build a sinusoidal model from a real-world scenario (identify A, B, C, D from context)
- Interpret period, amplitude, and midline in applied contexts
- Solve sinusoidal equations for specific output values within a domain
- Analyze rates of change of periodic functions over intervals
Topics in this unit
Learning objectives
- Convert between rectangular and polar coordinates
- Graph polar curves including circles, cardioids, and rose curves
- Represent curves using parametric equations x = f(t), y = g(t)
- Connect parametric and polar representations to periodic function behavior
Topics in this unit