Trig Tour
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Topics
- Trigonometry
- Unit circle
- Sines
- Cosines
- Tangents
Description
Take a tour of trigonometry using degrees or radians! Look for patterns in the values and on the graph when you change the value of theta. Compare the graphs of sine, cosine, and tangent.
Sample Learning Goals
- Define trig functions for negative angles and angles greater than 90 degrees.
- Translate between multiple representations of trig functions: as sides of a right triangle inscribed in a unit circle, graph of the function vs. angle, and numerical values of the function.
- Deduce the sign (+, -, 0) of a trig function for any given angle without a calculator using the unit circle concept.
- Estimate the value of trig functions for any given angle without a calculator using the unit circle concept.
- Define exact trig functions for special angles using degrees or radians for angle measures.
Standards Alignment
Common Core - Math
HSF-TF.A.2
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
HSF-TF.A.3
(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in terms of their values for x, where x is any real number.
HSF-TF.A.4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Version 1.0.14
Teacher Tips
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Overview of sim controls, model simplifications, and insights into student thinking ( PDF ). |
Teacher-Submitted Activities
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Authors | Level | Type | Subject |
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| Trig Tour - Connecting the Unit Circle to the Graph |
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Susan Miller | HS | Guided | Mathematics |
| Trig Tour - Seeing Patterns in a Unit Circle |
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Susan Miller | HS | Guided | Mathematics |
| Trig Tour - Using Reference Angles with a Unit Circle |
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Susan Miller | HS | Guided | Mathematics |
| CCSS Math Alignment with Sims |
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Amanda McGarry | MS K-5 HS |
Other | Mathematics | |
| Preguntas de razonamiento para todas las simulaciones HTML5 |
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Diana López | UG-Intro K-5 Grad HS UG-Adv MS |
HW Discuss |
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| Design Team | Third-party Libraries | Thanks To |
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