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Section 7.3 Double-Angle, Half-Angle and Product-Sum Formulas

Section 7.3 Double-Angle, Half-Angle and Product-Sum Formulas. Objectives: To understand and apply the double-angle formula. To understand and apply the half-angle formula. To understand and apply product-sum formula. Class Work . Evaluate csc780  Find the exact value of tan165.

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Section 7.3 Double-Angle, Half-Angle and Product-Sum Formulas

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  1. Section 7.3Double-Angle, Half-Angle and Product-Sum Formulas Objectives: To understand and apply the double-angle formula. To understand and apply the half-angle formula. To understand and apply product-sum formula.

  2. Class Work • Evaluate csc780 • Find the exact value of tan165

  3. Double-Angle Formulas Formula for sine: Formula for cosine: Formula for tangent:

  4. Ex 1. If and x is in quadrant II, find cos 2x, sin 2x, and tan 2x.

  5. Ex 2. If and x is in quadrant I, then find sin 2x, cos 2x, and tan 2x.

  6. Class Work 3. If and x is in quadrant II, find sin 2x, cos 2x, and tan 2x.

  7. Half-Angle Formulas

  8. Ex 3. Find the exact value of sin 22.5.

  9. Ex 4. Find

  10. Ex 5. Find if and u is in quad II.

  11. Class Work 4. Find if and u is in quad IV.

  12. Simplify the expression by using a double-angle or half-angle formula. 5. 6. 7.

  13. Product-to-Sum Formulas

  14. Ex 6. Express as a sum of trig functions.

  15. Ex 7. Compute sin 15 cos 15.

  16. Class Work 8. Write the product as a sum. 9. Compute:

  17. Sum-to-Product Formulas

  18. EX 8. Write as a product.

  19. Class Work 10. Write as a product.

  20. HW #2 p 548 1-7 odd, 15-23 odd, 27-31 odd, 35-57 odd.

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