Maryland Math F.TF.C.9.a
The Standard
Use trigonometric identities to rewrite expressions and as a tool when solving trigonometric equations.
Maryland College and Career Ready Standards for Mathematics (2025) · Prove and apply trigonometric identities.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite trigonometric expressions using identities, such as replacing 1 − cos²x with sin²x. They use the new form to solve equations and find all angles in a given interval.
What Mastery Looks Like
- A student can solve 1 − cos²x = 1/4 for 0 ≤ x < 2π by rewriting the left side as sin²x. They find all four angles and check them in the original equation.
Common Misconceptions
- Students may read sin²x as sin(x²) or forget that taking a square root gives both positive and negative values. Dividing by sin x can also discard solutions when sin x = 0.
How to Assess It
- Exit ticket: Solve 1 − sin²x = 1/4 for 0 ≤ x < 2π. Name the identity you used and check one answer in the original equation.
Lesson moves
Ways to Teach It
Give pairs unit-circle coordinate cards; have them calculate sin²θ + cos²θ for each card, then rewrite 1 − cos²θ.
Ask students to explain in writing why dividing sin x cos x = sin x by sin x loses an answer.
Have teams race to match cards labeled 1 − sin²x, cos²x, 1 − cos²x, and sin²x, then justify each match.
Draw a unit-radius Ferris wheel; use sin²θ + cos²θ = 1 to find seat heights when the horizontal offset is 0.5 meter.
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Printable F.TF.C.9.a Worksheet
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