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

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Algebra/Trig Reviewwe see−1 ⎛ 1 ⎞ πsin ⎜− ⎟=−⎝ 2⎠6−14. tan ( 1)SolutionThe restriction for inverse tangent is−1π πθ = tan ( x)− < θ
Algebra/Trig Review5.⎛cos cos⎜⎝⎛⎜⎝−1 32⎞⎞⎟⎟⎠⎠SolutionRecalling the answer to Problem 1 in this section the solution to this problem is mucheasier than it look’s like on the surface.⎛ ⎛1 3⎞⎞−⎛π⎞ 3cos cos = cos =⎜ ⎜⎜ ⎟2 ⎟⎟ ⎝ ⎝ ⎠⎠⎝ 6 ⎠ 2This problem leads to a couple of nice facts about inverse cosine−1 −1cos cos x = x AND cos cos θ = θ( ( )) ( ( ))6.1 ⎛πsin sin 4− ⎛ ⎞⎞⎜ ⎜ ⎟⎟⎝ ⎝ ⎠⎠SolutionThis problem is also not too difficult (hopefully…).−1⎛⎛π⎞ ⎞ −1 2 πsin sin sin⎛ ⎞⎜ ⎜ ⎟ = =4⎟⎝ ⎝ ⎠⎠ ⎜ 2 ⎟⎝ ⎠ 4As with inverse cosine we also have the following facts about inverse sine.−1 −1sin sin x = x AND sin sin θ = θ( )−17. tan tan ( 4)− .( ( )) ( ( ))SolutionJust as inverse cosine and inverse sine had a couple of nice facts about them so doesinverse tangent. Here is the fact−1 −1tan tan x = x AND tan tan θ = θ( ( )) ( ( ))−1Using this fact makes this a very easy problem as I couldn’t do tan ( 4)by hand! Acalculator could easily do it but I couldn’t get an exact answer from a unit circle.−1tan tan − 4 =− 4( ( ))Exponentials / LogarithmsBasic Exponential Functions© 2006 Paul Dawkins 81http://tutorial.math.lamar.edu/terms.aspx
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Algebra/Trig ReviewIntroductionThis
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Algebra/Trig Review26. ( ) 2x+ y+ 5
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Page 59 and 60: Algebra/Trig ReviewSolutionCotangen
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
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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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