Algebra/Trig Review - Pauls Online Math Notes - Lamar University

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Algebra/Trig ReviewNotice that the graph is always greater than 1 and less than -1. This should not be−1 ≤cos x ≤ 1. So, 1 divided by something less thanterribly surprising. Recall that ( )1 will be greater than 1. Also, 1 1±1 = ± and so we get the following ranges out ofsecant.Rsec ωx ≥R and Rsecωx ≤− R8. y = csc( x)( ) ( )SolutionFor this graph we will have to avoid x’s where sine is zerograph of cosecant will not exist forx = , −2 π, −π,0, π,2 π,Here is the graph of cosecant.⎛ 1 ⎞⎜cscx = ⎟. So, the⎝ sin x ⎠Cosecant will have the same range as secant.Rcsc ωx ≥R and Rcscωx ≤− R9. y = cot ( x)( ) ( )© 2006 Paul Dawkins 58http://tutorial.math.lamar.edu/terms.aspx
Algebra/Trig ReviewSolutionCotangent must avoidx = , −2 π, −π,0, π,2 π,since we will have division by zero at these points. Here is the graph.Cotangent has the following range.−∞
Page 1 and 2:
Algebra/Trig ReviewIntroductionThis
Page 3 and 4:
Algebra/Trig ReviewSimplifying Rati
Page 5 and 6:
Algebra/Trig Review1 1 1 13− −
Page 7 and 8: Algebra/Trig Review⎧33 −8xif x
Page 9 and 10: Algebra/Trig ReviewTo convert radic
Page 11 and 12: Algebra/Trig ReviewSo, what do we d
Page 13 and 14: Algebra/Trig Review( )2f x =− x +
Page 15 and 16: Algebra/Trig Review⎛ f ⎞⎜ ⎟
Page 17 and 18: Algebra/Trig ReviewYou can memorize
Page 19 and 20: Algebra/Trig Review6.SolutionIn thi
Page 21 and 22: Algebra/Trig Review2. ( ) 2y = x+ 3
Page 23 and 24: Algebra/Trig ReviewWe could also us
Page 25 and 26: Algebra/Trig Review26. ( ) 2x+ y+ 5
Page 27 and 28: Algebra/Trig Review2 29. ( x+ 1 ) (
Page 29 and 30: Algebra/Trig Review12. y = xSolutio
Page 31 and 32: Algebra/Trig ReviewComplex numbers
Page 33 and 34: Algebra/Trig ReviewFrom this we see
Page 35 and 36: Algebra/Trig ReviewSo, now that we
Page 37 and 38: Algebra/Trig ReviewSo, the two inte
Page 39 and 40: Algebra/Trig Review3.23x−2x− 11
Page 41 and 42: Algebra/Trig ReviewIn this case we
Page 43 and 44: Algebra/Trig ReviewSolutionThis one
Page 45 and 46: Algebra/Trig Review4x+ 534x−2x
Page 47 and 48: Algebra/Trig ReviewRemember how the
Page 49 and 50: Algebra/Trig ReviewFrom this unit c
Page 51 and 52: Algebra/Trig ReviewNow, if we remem
Page 53 and 54: Algebra/Trig ReviewTo do this probl
Page 55 and 56: Algebra/Trig ReviewIf ω > 1we can
Page 57: Algebra/Trig ReviewIn the case of t
Page 61 and 62: Algebra/Trig Review2x = 1 ( + ( x))
Page 63 and 64: Algebra/Trig Reviewdetermine what t
Page 65 and 66: Algebra/Trig Review3Now, there are
Page 67 and 68: Algebra/Trig Review4π2πn− 4x= +
Page 69 and 70: Algebra/Trig ReviewSince we want th
Page 71 and 72: Algebra/Trig Reviewπw= + 2 π n, n
Page 73 and 74: Algebra/Trig ReviewI didn’t put i
Page 75 and 76: Algebra/Trig ReviewSo, using our ca
Page 77 and 78: Algebra/Trig ReviewThere’s anothe
Page 79 and 80: Algebra/Trig ReviewFrom this we can
Page 81 and 82: Algebra/Trig Review5.⎛cos cos⎜
Page 83 and 84: Algebra/Trig Reviewx3. List as some
Page 85 and 86: Algebra/Trig ReviewBasic Logarithmi
Page 87 and 88: Algebra/Trig ReviewSolutionlog b xb
Page 89 and 90: Algebra/Trig ReviewThe domain y = l
Page 91 and 92: Algebra/Trig ReviewIn each of the e
Page 93 and 94: Algebra/Trig Review1−3z7 + 15e= 1
Page 95 and 96: Algebra/Trig ReviewThe first step i
Page 97 and 98: Algebra/Trig Reviewx 2= e1−x2x= e
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Algebra/Trig Review - Pauls Online Math Notes - Lamar University

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