# Trig Chapter 4 to 6

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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
 Author: ht2lvu ID: 2595 Card Set: Trig Chapter 4 to 6 Updated: 2009-12-09 05:59:54 Tags: trigonometry Folders: Description: trig qtr. 2 finals Show Answers: