CCSS.Math.Content.HSF-TF.C.9
The standard
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Common Core State Standards for Mathematics
What this standard means
Students need to show where the angle sum and difference identities come from, not just memorize them. They should be able to build a proof using the unit circle, distance formula, right triangles, or known identities, then use the formulas to rewrite expressions and find exact trig values.
Mastery looks like clear proof steps, correct signs, and smart use of identities to solve problems. Students often mix up sine and cosine patterns, lose negative signs, or treat tangent as separate instead of deriving it from sine over cosine.
Ways to teach it
- Have students use unit-circle coordinates and the distance formula to prove the cosine difference formula with two marked angles.
- Prompt students to explain why sine of a sum is not found by adding the two sine values.
- Give a 5-minute exit ticket asking for exact values of sin 75°, cos 15°, and tan 105°.
- Connect the formulas to rotating a point on a coordinate grid, then predict its new coordinates after two turns.
Plan a lesson for CCSS.Math.Content.HSF-TF.C.9
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Related standards
- 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.HSG-SRT.D.10
(+) Prove the Laws of Sines and Cosines and use them to solve problems.
- CCSS.Math.Content.HSF-TF.C
Prove and apply trigonometric identities
- CCSS.Math.Content.HSG-SRT.D.11
(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, result...