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Using Fundamental Trig Identities

Using Fundamental Trig Identities. Verifying Identities And Solving Trig Equations By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: December 29, 2009. Reciprocal Identities. Quotient Identities. Pythagorean Identities. Co function Identities.

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Using Fundamental Trig Identities

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  1. Using FundamentalTrig Identities Verifying Identities And Solving Trig Equations By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: December 29, 2009

  2. Reciprocal Identities

  3. Quotient Identities

  4. Pythagorean Identities

  5. Cofunction Identities Complimentary Angles

  6. Even/Odd Identities EVEN ODD

  7. Use the given to evaluate all six trig functions First determine that quadrant the given information holds true……. What quadrant is cotangent negative and sine positive??? II tangent

  8. Simplify a Trig Expression

  9. Verify a Trig Identity Work on one side only! Work DOWN the page, not across!

  10. Verify a Trig Identity Use the table feature and graphing utility to check your result. Select the path style for y2 so you can see the tracing

  11. Verify a Trig Identity

  12. Factoring Trig Expressions

  13. Factoring Trig Expressions

  14. Factoring Trig Expressions

  15. Factoring Trig Expressions

  16. Factoring Trig Expressions

  17. Add & Subtract Trig Expressions

  18. Add & Subtract Trig Expressions

  19. Add & Subtract Trig Expressions

  20. Verify Trig Identities

  21. Verify Trig Identities - Guidelines • Work with one side of the equation at a time. It is often better to work with the more complicated side first. • Look for opportunities to factor an expression, add fractions, square a binomial, or create a monomial denominator. • Look for opportunities to use the fundamental identities. Note which functions are in the final expression you want. Sines and cosines pair up well, as do secants with tangents, and cosecants with cotangents. • If the preceding guidelines do not help, try converting all terms to sines and cosines. • Always try something. Even making an attempt that leads to a dead end provides insight.

  22. Verify Trig Identities

  23. Verify Trig Identities

  24. Verify Trig Identities

  25. Verify Trig Identities

  26. Verify Trig Identities

  27. Verify Trig Identities

  28. Verify Trig Identities

  29. Verify Trig Identities

  30. Verify Trig Identities

  31. Verify Trig Identities

  32. Solving Trig Equations

  33. Solving Trig Equations

  34. Solving Trig Equations

  35. Solving Trig Equations

  36. Solving Trig Equations

  37. Solving Trig Equations

  38. Solving Trig Equations

  39. Sum & Difference Formulas

  40. Sum & Difference Formulas

  41. R (x2, y2 ) (cos(A+B), sin(A+B) ) Proof of cos(A+B) = cosA•cosB - sinA•sinB Q (x1, y1)  (cosA, sinA) B Q (x1, y1) S (x3, y3) (cos(-B), sin(-B) ) R (x2, y2 ) A P (1, 0) -B S (x3, y3)

  42. Proof ofsin(A+B) = sinA•cosB + cosA•sinB Note: This proof uses the cofunction identities.

  43. Use Sum & Difference Formulas Find the exact value of sin(750)

  44. Use Sum & Difference Formulas Find the exact value of:

  45. Use Sum & Difference Formulas Find the exact value of: Rationalize the denominator

  46. Use Sum & Difference Formulas Simplfy:

  47. Use Sum & Difference Formulas Find the exact value of sin(u+v) given the following:

  48. Verify Trig Identities

  49. Solving Trig Equations on [0, 2π)

  50. Double-Angle Formulas

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