CCSS.Math.Content.HSF-TF.A.3
The standard
(+) 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 π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.
Common Core State Standards for Mathematics
What this standard means
Students need to connect 30-60-90 and 45-45-90 triangles to exact trig values, not just memorize a chart. They should know why sin, cos, and tan for π/6, π/4, and π/3 have those values, then use the unit circle to find related angles by symmetry.
Mastery looks like giving exact values quickly and explaining the sign and reference angle. Students often mix up sine and cosine, forget tangent is y over x, or lose the negative sign for angles in quadrant III or IV.
Ways to teach it
- Have students build 30-60-90 and 45-45-90 triangles on grid paper, label side lengths, then place them on the unit circle.
- Ask students to explain why sin(π + x) is negative when sin(x) is positive, using a unit circle sketch.
- Give a 6-question exit ticket with exact values for sin(π/6), cos(7π/6), tan(5π/4), and similar angles.
- Connect to a Ferris wheel model by marking positions at π/6, π/4, π/3, π + x, and 2π - x.
Plan a lesson for CCSS.Math.Content.HSF-TF.A.3
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSF-TF.A
Extend the domain of trigonometric functions using the unit circle
- CCSS.Math.Content.HSF-TF.B.7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms...
- 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.C.9
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.