Study Guide — HSF.TF.C.8

Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi…

Use the unit circle and trig ratios to model periodic phenomena.

What this standard means

• 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.
• Apply prove the pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… with models and explanation
• Evaluates trig functions at standard angles

_See printable PDF for diagram._

How to use the 20 practice sets

| Sets | When to use | | --- | --- | | 1–5 | Intro — explore together, short written items | | 6–10 | Core skills — diagrams and written practice | | 11–15 | Mixed review — explain thinking | | 16–20 | Stretch — word problems and mastery tasks |

Pacing: 10–15 minutes per session.

How to practice

1. Label unit circle coordinates for key angles 2. Connect radians and degrees 3. Graph sine and cosine with amplitude and period

_See printable PDF for diagram._

Common mistakes

• Wrong quadrant signs
• Period or amplitude errors in graphs

Review and practice tests

1. Start Review 1/10 when sets 1–3 feel comfortable. 2. Move up one review level with little help. 3. Use Practice Test 4/10–6/10 for mid-standard checks. 4. Practice Test 10/10 is the mastery bar for HSF.TF.C.8.

• [ ] Evaluates trig functions at standard angles
• [ ] Uses unit circle reasoning
• [ ] Graphs basic trig functions with transformations

Materials for this standard

• Practice Problems — 20 printable sets
• Review — 10 difficulty levels
• Practice Test — 10 difficulty levels
• Answer key — for parents and tutors