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

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