Common Core · High school
HSF-TF.C.9
High school — Prove the addition and subtraction formulas for sine, cosine and tangent and use them to solve problems.
A note on this mapping: HSF-TF.C.9 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The 2 skills that cover it
- Trigonometric IdentitiesUse the Pythagorean and quotient identities to simplify expressions and verify equations.Read the lesson →
- Half-Angle & Product IdentitiesFinish the identity toolkit: the half-angle formulas and their signs, the power-reducing formulas, product-to-sum and sum-to-product, tan(t/2), and verifying an identity with all of them.Read the lesson →
What a student should be able to do
- Apply sin2 t + cos2 t = 1 and its rearrangements.
- Use the quotient and reciprocal identities.
- Simplify a trigonometric expression to a single function.
- Verify an identity step by step.
- Find exact values such as sin 15° and cos(π/8) with a half-angle formula, choosing the sign from the quadrant.
- Given one ratio of t and an interval for t, find sin(t/2), cos(t/2) or tan(t/2).
- Rewrite powers of sine and cosine with the power-reducing formulas, and convert between products and sums.
- Verify an identity or evaluate an expression using the half-angle, product-to-sum and sum-to-product formulas.