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Ch5.1A – Using Fundamental Identities Reciprocal Identities Quotient Identities

Ch5.1A – Using Fundamental Identities Reciprocal Identities Quotient Identities Pythagorean Identities sin 2 u + cos 2 u = 1 1 + tan 2 u = sec 2 u 1 + cot 2 u = csc 2 u. Cofunction Identities Even/Odd Identities Even Odd cos (–u) = cos (u) sin(–u) = – cos (u)

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Ch5.1A – Using Fundamental Identities Reciprocal Identities Quotient Identities

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  1. Ch5.1A – Using Fundamental Identities Reciprocal Identities Quotient Identities Pythagorean Identities sin2u + cos2u = 1 1 + tan2u = sec2u 1 + cot2u = csc2u

  2. Cofunction Identities Even/Odd Identities EvenOdd cos(–u) = cos(u) sin(–u) = –cos(u) sec(–u) = sec(u) tan(–u) = –tan(u) cot(–u) = –cot(u) csc(–u) = –csc(u)

  3. Ex1) find all six trigs. Ex2) Simplify: sinx.cos2x – sinx

  4. Ex3) Use ur calc to determine if the following are identities: a) cos3x = 4cos3x – 3cosx b) cos3x = sin(3x – ) Ex4) Verify by hand: Ch5.1A p414 19 – 43odd

  5. Ch5.1A p414 19 – 43odd Do 19,21,29,31,37,39,41 in class

  6. Ch5.1B – More Identities Ex5) Factor: a) sec2θ – 1 b) 4tan2θ + tanθ – 3 Ex6) Factor: csc2x – cotx – 3

  7. Ex7) Simplify: sint + cott.cost Ex8) Rewrite not as a fraction

  8. Ex9) If x = 2tanθ, use substitution to express as a trig function. (0 < θ < π/2) Ch5.1B p414 45-63odd,71-75odd

  9. Ch5.1B p414 45-63odd,71-75odd

  10. Ch5.1C p414 20 – 62 even

  11. Ch5.2A – Verifying Trig Identities Guidelines: 1. Work one side at a time, usually the most complicated 1st. 2. Look to: - Factor - Add fractions - Square a binomial - Get a monomial denominator 3. Use fundamental identities 4. Head toward sine and cosine 5. But try SOMETHING!

  12. Ex1) Verify:

  13. Ex2) Verify:

  14. Ex3) Verify: (tan2x + 1)(cos2x – 1) = –tan2x

  15. Ex4) Verify: tanx + cotx = secx.cscx

  16. HW#25) Verify: Ch5.2A p421 1 – 10 all

  17. Ch5.2A p421 1 – 10 all

  18. Ch5.2B – More Verifying Trig ID’s Ex5) Verify:

  19. Ex6) Verify:

  20. Ex7) Verify: tan4x = tan2x.sec2x – tan2x Verify: sin3x.cos4x = (cos4x – cos6x).sinx

  21. HW#46) Verify: Ch5.2B p421 21 – 39 odd

  22. Ch5.2B p421 21 – 39 odd

  23. Ch5.2C p422 40-48all

  24. Ch5.3A – Solving Trig Functions Ex1) Solve: 2sinx – 1 = 0 Ex2) Solve:

  25. Ex3) Solve: 3tan2x – 1 = 0 Ex4) Solve: cotx.cos2x = 2cotx

  26. Ex5) Solve: 2sin2x – sinx – 1 = 0 over [0,2π] Ex6) Solve: 2sin2x + 3cosx – 3 = 0 Ch5.3A p431 11 – 29odd,60

  27. Ch5.3A p431 11 – 29odd,60

  28. Ch5.3B – Solving Trig Functions cont HW#18) Solve: tan23x = 3 #24) Solve: cos2x.(2cosx + 1) = 0

  29. #35) Solve: #37) Solve: Ch5.3B p432 12 – 24even, 31 – 37odd

  30. Ch5.3B p432 12 – 24even, 31 – 37odd

  31. Ch5.4A – Sum and Difference Formulas sin(u + v) = sinu.cosv + cosu.sinv sin(u – v) = sinu.cosv – cosu.sinv cos(u + v) = cosu.cosv– sinu.sinv cos(u – v) = cosu.cosv +sinu.sinv Ex1) Find the exact value of cos75˚.

  32. sin(u + v) = sinu.cosv + cosu.sinv sin(u – v) = sinu.cosv – cosu.sinv cos(u + v) = cosu.cosv– sinu.sinv cos(u – v) = cosu.cosv +sinu.sinv Ex2) Find the exact value of , given that

  33. sin(u + v) = sinu.cosv + cosu.sinv sin(u – v) = sinu.cosv – cosu.sinv cos(u + v) = cosu.cosv– sinu.sinv cos(u – v) = cosu.cosv +sinu.sinv Ex3) Find the exact value of sin42˚.cos12˚ – cos42˚.sin12˚

  34. sin(u + v) = sinu.cosv + cosu.sinv sin(u – v) = sinu.cosv – cosu.sinv cos(u + v) = cosu.cosv– sinu.sinv cos(u – v) = cosu.cosv +sinu.sinv Ex4) Prove the cofunction identity

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