CCSS.Math.Content.HSF-TF.A
The standard
Extend the domain of trigonometric functions using the unit circle
Common Core State Standards for Mathematics · High School — Functions
What this standard means
Students need to connect angles to points on the unit circle, then use those points to define sine, cosine, and tangent for angles beyond 0 to 90 degrees. They should work in radians and degrees, understand coterminal angles, and see why trig values repeat.
Mastery looks like finding trig values from the unit circle, explaining signs by quadrant, and using reference angles without guessing. Students often get stuck converting radians, mixing up x and y coordinates, and treating the unit circle as a chart to memorize instead of a definition.
Ways to teach it
- Have students build a paper unit circle with string radius, mark key angles, then label coordinates, sine, cosine, and tangent signs.
- Ask students to explain why sin 30 degrees equals sin 150 degrees, but cos 30 degrees does not equal cos 150 degrees.
- Give five angles, including negative and over 360 degrees, and have students write a coterminal angle plus the sine and cosine signs.
- Connect unit circle motion to a Ferris wheel by matching height above center to sine values at different rotation angles.
Plan a lesson for CCSS.Math.Content.HSF-TF.A
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Related standards
- CCSS.Math.Content.HSF-TF.B.6
(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- CCSS.Math.Content.HSF-TF.A.4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
- CCSS.Math.Content.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 ...
- CCSS.Math.Content.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 angl...