Curriculum placement
Algebra 2. This describes the skill, not a learner estimate.
Choosing a periodic model
Choose trigonometric models with appropriate amplitude frequency and midline
Problem types
- Build a periodic model
- Write the cosine equation of a graphed periodic model
Builds on
- Period, amplitude, and midline
- Comparing functions given in different forms · Useful idea
A periodic model can be given as a table, graph or equation, and its amplitude and period are read from any of them.
- Checking a model against evidence · Useful idea
Residual patterns apply to any model, including a sine or cosine model whose midline, amplitude and period are checked against measurements.
- Solving trigonometric equations · Useful idea
Setting a sinusoidal model equal to a value and solving gives the times at which the modeled quantity reaches that value.
- Average rate of change · Useful idea
The average rate of change of a periodic model over an interval measures how fast it rises or falls on average.
Leads to
- Motion described by a parameter · Extend the idea
A rider on a wheel has a height that is a sinusoid of time. Pairing it with a second sinusoid for horizontal position describes the whole circular path as a function of one parameter.
Related skills
- Quadratic, rational, and exponential constraints · Related idea
Choosing a model for a situation includes choosing between a quadratic, exponential and sinusoid.
- Matrices as transformations of the plane · Related idea
A rotation matrix with entries cosine and sine turns each point by an angle, the same periodic pattern as a sinusoid.
- Velocity and force as vectors · Related idea
The position of a point moving around a circle is a vector whose components are a cosine and a sine of time.
- Reading slope and intercept in context · Related idea
Fitting a sinusoid to data is a nonlinear regression, and a line fit is the linear case.
- Inverse trigonometric functions · Shared foundations
Open the interactive map to explore lessons and skill connections.