CCSS.Math.Content.HSF-TF.C
The standard
Prove and apply trigonometric identities
Common Core State Standards for Mathematics · High School — Functions
What this standard means
Students need to use known relationships among sine, cosine, tangent, and the Pythagorean identity to rewrite expressions, prove identities, and solve problems. They should understand that an identity is true for every allowed input, not just for a few angle values.
Mastery looks like choosing useful substitutions, showing each algebra step, and checking restrictions where denominators are involved. Students often get stuck treating an identity like an equation to solve, dropping squared terms incorrectly, or using memorized formulas without knowing when they apply.
Ways to teach it
- Give pairs identity card strips, such as tan x, sin x over cos x, and 1 minus sin squared x, and have them build valid proof chains.
- Ask students to write: How is proving an identity different from solving a trig equation? Include one example of each.
- Post three short identity proofs with one hidden error each, and have students mark the first invalid step on a sticky note.
- Use a Ferris wheel height model and have students rewrite the equation using a cofunction or Pythagorean identity to answer the same question.
Plan a lesson for CCSS.Math.Content.HSF-TF.C
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Related standards
- CCSS.Math.Content.HSG-CO.C
Prove geometric theorems
- CCSS.Math.Content.HSG-SRT.D.10
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
- CCSS.Math.Content.HSG-SRT.D
Apply trigonometry to general triangles
- CCSS.Math.Content.HSF-TF.C.8
Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.