Trig Chapter 4 to 6

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Author:
ht2lvu
ID:
2595
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Trig Chapter 4 to 6
Updated:
2009-12-09 00:59:54
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trigonometry
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Description:
trig qtr. 2 finals
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  1. function
    • special kind of relationship
    • ratio dependent on angle
  2. amplitude
    height of wave (can't be negative)
  3. y=a sin x, amplitude
    • a
    • coefficient of trig function
  4. period
    how long it takes to complete a full cycle
  5. y=sin bx, period
    • b
    • coefficient of angle portion
  6. negative function
    flip graph
  7. steps to graphing function graph
    • 1.horizontal translation
    • 2. end of full cycle
    • 3. half of cycle
    • 4. quarter of cycle
    • 5. all other tickmarks
    • 6. new x-axis (v.t.)
    • 7. max value
    • 8. min value
    • 9. graph & check
  8. steps to graph csc & sec
    • 1. use sin/cos as guide function
    • 2. sketch sin/cos graph
    • 3. sketch vertical asymptotes
    • 4. sketch csc/sec graph
  9. steps to graph tan
    • 1. determine period
    • 2. sketch vertical asymptotes
    • 3. sub-divide the interval into four equal parts
    • 4. find values at 1st qtr, midpoint, 3rd qtr point
    • 5. join points with smooth curve that approaches vertical asymptotes
    • 6. check values
  10. period of sin/cos
    2pi
  11. period of tangent
    pi/b
  12. steps to graph cot
    • 1. determine period
    • 2. sketch vertical asymptotes
    • 3. sub-divide the interval into four parts
    • 4. find values at 1st qtr point, midpoint, 3rd qtr point
    • 5. join points with smooth curve
    • 6. check values
  13. reciprocal identities
    • sin theta= 1/ csc theta
    • csc theta=1/sin theta
    • cos theta=1/sec theta
    • sec theta=1/cos theta
    • tan theta=1/cot theta
    • cot theta=1/tan theta
  14. quotient identities
    • tan theta=sin theta/cos theta
    • cot theta=cos theta/sin theta
  15. pythagorean identitites
    • sin2theta+cos2theta=1
    • 1+tan2theta=sec2theta
    • cot2theta+1=csc2theta
  16. negative angle identities
    • sin theta=-sin(-theta)
    • cos theta=cos (-theta)
    • tan theta= -tan (-theta)
    • csc theta= -csc (-theta)
    • sec theta= sec (-theta)
    • cot theta= -cot (-theta)
  17. hints for verifying identities
    • 1. make more complicated (longer) side simpler (shorter)
    • 2. change all trig functions to sine and cosine, then simplify
    • 3. factor
    • 4. side you're not changing is your goal
    • 5. if expression has 1+sin x, multiplying numerator & denominator by 1-sin x would give cos2x
  18. difference identity for cosine
    cos(A-B)=cosA cosB + sinA sinB
  19. sum identity for cosine
    cos(A+B)=cosA cosB - sinA sinB
  20. cofunction identities
    • cos(90-theta)=sin theta
    • sin(90-theta)=cos theta
    • tan(90-theta)=cot theta
    • cot(90-theta)=tan theta
    • sec(90-theta)=csc theta
    • csc(90-theta)=sec theta
  21. sum identitiy for sine
    sin(A+B)= sinA cosB + cosA sinB
  22. difference identity for sine
    sin(A-B)= sinA cosB - cosA sinB
  23. sum identity for tangent
    tan(A+B)= tanA + tanB / 1- tanA tanB
  24. difference identity for tangent
    tan(A-B)= tanA - tanB/ 1+ tanA tanB
  25. double angle identities for cosine
    • cos2A= cos2A - sin2A
    • cos2A= 2cos2A - 1
    • cos2A= 1 - 2sin2A
  26. double angle identity for sine
    sin2A= 2sinAcosA
  27. double angle identity for tangent
    tan2A= 2tanA / 1-tan2A
  28. half angle identity for cosine
    cos theta/2= +/- root 1+cos theta/2
  29. half angle identity for sine
    sin theta/2= +/- root 1-cos theta/2
  30. half angle identities for tangent
    • tan theta/2= +/- root 1-cos theta/1+cos theta
    • sin theta/ 1+cos theta
    • 1-cos theta/ sin theta

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