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Learning Goal
‹2 of 2 in this cluster
Prove angle sum formulas
Start lessonBegins with Cos subtraction proof and derivations · Slides
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
HSF.TF.C.9
**HSF.TF.C.9**: (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
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HSF.TF.C.9: (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
What you'll learn
- State the angle addition formulas: sin(A + B) = sin(A)cos(B) + cos(A)sin(B) and cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- Follow a geometric proof of cos(A - B) using the distance formula on the unit circle
- Derive sin(A + B) from cos(A + B) using the co-function relationship sin(theta) = cos(pi/2 - theta)
- Use the addition formulas to find exact values of non-standard angles (e.g., sin(75 degrees) = sin(45 + 30))
- Derive the double angle formulas as special cases: sin(2A) = 2 sin(A)cos(A) and cos(2A) = cos^2(A) - sin^2(A)
- Derive the tangent addition formula tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B))
Review first:
Slides
Step through the lesson, or watch it as a narrated video • 2 slide decks
1
Cos subtraction proof and derivations
✓ Start here2
Exact values and double angle
Practice
Try it on your own
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