# Trig Chapter 4 to 6

 function special kind of relationshipratio dependent on angle amplitude height of wave (can't be negative) y=a sin x, amplitude acoefficient of trig function period how long it takes to complete a full cycle y=sin bx, period bcoefficient of angle portion negative function flip graph steps to graphing function graph 1.horizontal translation2. end of full cycle3. half of cycle4. quarter of cycle5. all other tickmarks6. new x-axis (v.t.)7. max value8. min value9. graph & check steps to graph csc & sec 1. use sin/cos as guide function2. sketch sin/cos graph3. sketch vertical asymptotes4. sketch csc/sec graph steps to graph tan 1. determine period2. sketch vertical asymptotes3. sub-divide the interval into four equal parts4. find values at 1st qtr, midpoint, 3rd qtr point5. join points with smooth curve that approaches vertical asymptotes6. check values period of sin/cos 2pi period of tangent pi/b steps to graph cot 1. determine period2. sketch vertical asymptotes3. sub-divide the interval into four parts4. find values at 1st qtr point, midpoint, 3rd qtr point5. join points with smooth curve6. check values reciprocal identities sin theta= 1/ csc thetacsc theta=1/sin thetacos theta=1/sec thetasec theta=1/cos thetatan theta=1/cot thetacot theta=1/tan theta quotient identities tan theta=sin theta/cos thetacot theta=cos theta/sin theta pythagorean identitites sin2theta+cos2theta=11+tan2theta=sec2thetacot2theta+1=csc2theta 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) hints for verifying identities 1. make more complicated (longer) side simpler (shorter)2. change all trig functions to sine and cosine, then simplify3. factor4. side you're not changing is your goal5. if expression has 1+sin x, multiplying numerator & denominator by 1-sin x would give cos2x difference identity for cosine cos(A-B)=cosA cosB + sinA sinB sum identity for cosine cos(A+B)=cosA cosB - sinA sinB cofunction identities cos(90-theta)=sin thetasin(90-theta)=cos thetatan(90-theta)=cot thetacot(90-theta)=tan thetasec(90-theta)=csc thetacsc(90-theta)=sec theta sum identitiy for sine sin(A+B)= sinA cosB + cosA sinB difference identity for sine sin(A-B)= sinA cosB - cosA sinB sum identity for tangent tan(A+B)= tanA + tanB / 1- tanA tanB difference identity for tangent tan(A-B)= tanA - tanB/ 1+ tanA tanB double angle identities for cosine cos2A= cos2A - sin2Acos2A= 2cos2A - 1cos2A= 1 - 2sin2A double angle identity for sine sin2A= 2sinAcosA double angle identity for tangent tan2A= 2tanA / 1-tan2A half angle identity for cosine cos theta/2= +/- root 1+cos theta/2 half angle identity for sine sin theta/2= +/- root 1-cos theta/2 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 Authorht2lvu ID2595 Card SetTrig Chapter 4 to 6 Descriptiontrig qtr. 2 finals Updated2009-12-09T05:59:54Z Show Answers