CCSS.Math.Content.HSF-TF.A

CCSS.Math.Content.HSF-TF.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSF-TF.A.1

  Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

• 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...

• 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.4

  (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

01

What Students Need to Do

Students connect real-number inputs to rotations measured in radians on the unit circle. They find exact trigonometric values and use coordinates to explain symmetry, signs, and periodic behavior.

02

What Mastery Looks Like

Students locate positive and negative radian measures on the unit circle and give exact sine, cosine, and tangent values. They use reference angles, symmetry, and full rotations to explain repeated values and sign changes.

03

Common Misconceptions

Students often mix degrees and radians, swap sine and cosine coordinates, or lose signs outside the first quadrant. They may also think adding 2π changes the function value or forget that tangent is undefined when cosine is zero.

04

How to Assess It

Give this exit ticket: For θ = -5π/6, plot the unit-circle point, find sine and cosine, then explain what happens at θ + 2π.

1. 01

   Wrap string cut to one radius around a paper circle, marking each radius-length arc to build radian measures.

2. 02

   Ask students to write why sine stays unchanged when 2π is added, using unit-circle coordinates as evidence.

3. 03

   Play a card match with radian angles, unit-circle points, reference angles, and exact trigonometric values.

4. 04

   Model a Ferris wheel seat with a rotating point, then connect its height to the point’s sine value over time.

• 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.