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MAT170 SPR 2009 Material for 3rd Quiz. Study Pages. Sum and Difference Identities: ( sin ). sin (a ± b) = sin (a) cos (b) ± cos (a) sin (b). sin (a + b) = sin (a) cos (b) + cos (a) sin (b) sin (a - b) = sin (a) cos (b) - cos (a) sin (b). Sum and Difference Identities: ( cos ).

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Study Pages

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  1. MAT170 SPR 2009 Material for 3rd Quiz Study Pages

  2. Sum and Difference Identities:(sin) sin (a ± b) = sin(a)cos(b) ± cos(a)sin(b) sin (a + b) = sin(a)cos(b) +cos(a)sin(b) sin (a - b) = sin(a)cos(b) -cos(a)sin(b)

  3. Sum and Difference Identities:(cos) cos(a ± b) = sin(a)sin(b) ± cos(a)cos(b) cos (a + b) = sin(a)sin(b) - cos(a)cos(b) cos (a - b) = sin(a)sin(b) + cos(a)cos(b) 

  4. Pythagorean Identities

  5. Reciprocal Identities

  6. Quotient Identities

  7. Even-Odd Identites

  8. Functions sin & cos

  9. Functions tan & cot

  10. Functions sec & csc:

  11. Which Function goes with the graph? • sincrosses the Y axisat midpoint • coscrosses the Y axisat high (or low) point • sec and tancross the y axis • csc and cot have asymptotes at Y axis

  12. How to findCoterminal Angles: • Coterminal = Given ± k(2π)+ if angle is negative- if angle is positive • K≈ Given /2π(round upif angle is negative, round downif angle is positive) • Remember: 2π = 360°

  13. Hint on finding Coterminal Angles in radians: • Coterminal = Θ ± k(2π)+ if angle is negative- if angle is positive • Convert 2π to match denominators with Θ, then k is easy to solve • 2π = 4π/2 = 6π/3 = 8π/4 = 12π/6

  14. How do you convert between radians and degrees? 180°= π So by dimensional analysis: X° (π/180 ° ) = Θ radians And Θ radians (180 °/π) = X°

  15. Formula for length of an arc: S = rΘ Θ must be in radians

  16. Linear speed of a point on a circle: V = S/t Distance/time Where S = RΘ

  17. A useful mnemonic for certain values of sines and cosinesFor certain simple angles, the sines and cosines take the form  for 0 ≤ n ≤ 4, which makes them easy to remember.

  18. 30º = П 6

  19. 45º = П 4

  20. 60º = П 3

  21. sinП6. = ½

  22. cosП6. =√3/2

  23. tanП6. =√3/3

  24. When you remember what is underneath, Click the shape to make certain. The Unit Circle

  25. SohCahToa: • sin Θ = Opposite Hypotenuse • Cos Θ = Adjacent Hypotenuse • Tan Θ = Opposite Adjacent . B Θ A C

  26. X = cosΘ Y = sin Θtan Θ = sin ΘcosΘ

  27. X = cosΘ Y = sin Θcot Θ = cosΘ sin Θ

  28. X = cosΘ Y = sin Θsec Θ = 1 .cosΘ

  29. X = cosΘ Y = sin ΘcscΘ = 1 . sin Θ

  30. Trig Co-function Identities: * Co-Function for Sine: * Co-Function for Cosine: * Co-Functions for Tangent: * Co-Function for Cotangent: * Co-Function for Secant: * Co-Function for Cosecant: • sin a = cos (π/2 – a) • cos a = sin (π/2 – a) • tan a = cot (π/2 – a) • cot a = tan (π/2 – a) • sec a = csc (π/2 – a) • csc a = sec (π/2 – a)

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