Number: MA.912.T.3
Title: Graph and apply trigonometric relations and functions.
Type:
Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Trigonometry
Related Benchmarks
This cluster includes the following benchmarks
| Code |
Description |
| MA.912.T.3.1: | Given a mathematical or real-world context, choose sine, cosine or tangent trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift and midline. |
| MA.912.T.3.2: | Given a table, equation or written description of a trigonometric function, graph that function and determine key features.Clarifications:
Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetry; end behavior; periodicity; midline; amplitude; shift(s) and asymptotes.Clarification 2: Instruction includes representing the domain and range with inequality notation, interval notation or set-builder notation.
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| MA.912.T.3.3: | Solve and graph mathematical and real-world problems that are modeled with trigonometric functions. Interpret key features and determine constraints in terms of the context.Clarifications:
Clarification 1: Key features are limited to domain; range; intercepts; intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetry; end behavior; periodicity; midline; amplitude; shift(s) and asymptotes.Clarification 2: Instruction includes representing the domain, range and constraints with inequality notation, interval notation or set-builder notation. Clarification 3: Instruction includes using technology when appropriate.
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Related Resources
Vetted resources educators can use to teach the concepts and skills in this topic.
Formative Assessment
| Name |
Description |
| Elevation Along a Trail: | Students are asked to interpret key features of a graph (symmetry) in the context of a problem situation. |
Lesson Plans
| Name |
Description |
| Ferris Wheel: | This lesson is intended to help you assess how well students are able to:
- Model a periodic situation, the height of a person on a Ferris wheel, using trigonometric functions.
- Interpret the constants a, b, c in the formula h = a + b cos ct in terms of the physical situation, where h is the height of the person above the ground and t is the elapsed time.
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| Tune In and Sine: | This lesson is intended to show students how to use the equations and graphs of sine and cosine to model real-world applications particularly using amplitude, period, and midline. |
| City Temperatures and the Cosine Curve: | Students will work with temperature data from San Antonio, Texas and Buenos Aires, Argentina. They will view the periodicity of the city temperatures and build cosine functions to fit the data. The function equation results are then used to find temperatures for a given day, or certain days for a given temperature. |
Perspectives Video: Expert
Problem-Solving Tasks
| Name |
Description |
| The Lighthouse Problem: | This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat. |
| Foxes and Rabbits 2: | This problem solving task challenges students to use trigonometric functions to model the number of rabbits and foxes as a function of time. |
| As the Wheel Turns: | In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context. |
Student Resources
Vetted resources students can use to learn the concepts and skills in this topic.
Perspectives Video: Expert
Problem-Solving Tasks
| Title |
Description |
| The Lighthouse Problem: | This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat. |
| Foxes and Rabbits 2: | This problem solving task challenges students to use trigonometric functions to model the number of rabbits and foxes as a function of time. |
| As the Wheel Turns: | In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context. |
Parent Resources
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
Problem-Solving Tasks
| Title |
Description |
| The Lighthouse Problem: | This problem asks students to model phenomena on the surface of the earth by examining the visibility of the lamp in a lighthouse from a boat. |
| Foxes and Rabbits 2: | This problem solving task challenges students to use trigonometric functions to model the number of rabbits and foxes as a function of time. |
| As the Wheel Turns: | In this task, students use trigonometric functions to model the movement of a point around a wheel and, through space. Students also interpret features of graphs in terms of the given real-world context. |
