Answer Key — HSF.TF.C.8

For parents and tutors

Do not share with students before practice tests.

Practice Problems — Sets 1–10

| Set | Guidance | | --- | --- | | Set 1 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 2 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 3 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 4 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 5 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 6 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 7 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 8 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 9 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 10 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. |

Practice Problems — Sets 11–20

| Set | Guidance | | --- | --- | | Set 11 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 12 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 13 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 14 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 15 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 16 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 17 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 18 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 19 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. | | Set 20 | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to fi… — verify written work and accept reasonable drawings. |

Review tiers 1–10

Checklists are parent-judged.
Written items: verify against practice set patterns.
Standard text: 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.

Practice test scoring

| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |

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