# Ferris Wheel: Trigonometric Functions

Grades 9-12 / Math / Functions
CCSS: Math.HSF-BF-A.1b Math.HSF-BF.B.3 Math.HSF-TF.A.1

Common Core State Standards

 Math Math HSF-BF-A High School: Functions: Building Functions 1b Build a function that models a relationship between two quantities Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. Download Common Core State Standards (PDF 1.2 MB)

Common Core State Standards

 Math Math HSF-BF High School: Functions: Building Functions B Build new functions from existing functions 3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Download Common Core State Standards (PDF 1.2 MB)

Common Core State Standards

 Math Math HSF-TF High School: Functions: Trigonometric Functions A Extend the domain of trigonometric functions using the unit circle 1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Download Common Core State Standards (PDF 1.2 MB)

### Objective

• Model how a trigonometric function describes the relationship of a Ferris wheel rider as the wheel spins at a constant rate with relationship to the height of the rider from the ground.
• Discern the relationship between the given measure and the period, phase, offset and amplitude of a cosine function.

15 min

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