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# Review Sheet for MATH 111 at UA 2

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This 6 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

Math 111 Trigonometry Practice Exam 2 Warning This study guide is not all inclusive there may be material on the test which is covered in the book but not here This is simply meant to be a supplemental study aid to the homework and class notes 1 Graph two periods of y 72 4cos7r 7 Find the amplitude period and average value Label the axes in a way to re ect the important characteristics of the graph ie when the function reaches it maximum minimum and average value 2 Below is a data table for a function involving a trigonometric function le110111213l4l y 3 7 11 7 3 7 Determine a possible formula for the trigonometric function Solution Here are two possibilities There are others y 7 4singz y 7 4cosgz 71 3 Consider a function with the below graph a Find a formula for this function involving sine Solution 7T y 1 2sin 71 b Find a formula for this function involving cosine 7r y cos 2 s Solution 4 Find the following exact values a The period of the function y tan4 7 3 Solution 7r4 b The horizontal shift of the function f 1 7 2 sin3 7 4 Solution 4 units to the right c The average value of the function g 2 7 2cos7r 7T Solution 2 d tancos 17 3 Solution 125 e cosarctan sin 1 Hint Use the Cosine of a Surn identity Solution 2fi 6 f sintan 1 Solution 3 13 5 Mark the following true or false a csc7z icscx Solution True since sin7x isinz b The amplitude of y 73 sin5 3 is 73 Solution False the amplitude is always positive 0 arctanz 3 arctanz 3 Solution False d tan 1 z arctanz Solution True 6 For each of the below expressions7 determine if the statement is possible or impossible For those that are possible7 determine the exact value Represent all angles in radians a arcsin 7139 Solution lmpossible domain of arcsin is 7171 b cos 17 Solution Possible7 and the value is 571396 C sin74 Solution Possible7 and the value is approximately 07568 d sin 130 Solution Impossible domain of arcsin is 71 7 Use the below graph of y sinx to approximately nd arcsin17 and mark this point on the appropriate axis 8 Find the domain and range of the following functions a y sin 1z 1 Solution Domain 7207 Range 7717277172 b y 3arccos Solution Domain 7227 Range 073 c y tan 1z 1 Solution Domain foo7 oo7 Range fa2 17T2 1 9 Find an expression for sintan 1 that does not involve trigonometric functions Solution w xwz 22 10 Find all solutions to cosa le nd all x values that make this statement true Which one is cos 1 i 11 12 13 Solution zi 5g27m T 27m The only solution that is in the interval 077139 the range of arccos m is z 7r37 so cos 112 7r3 Consider the following two statements a z sin 1 y always means y sinx b y sinx always means z sin 1 y ls statement a true or false ls statement b true or false Explain Solution Recall the de nition of inverse sine is that z sin ly means y sinx AND z E 77r27 7r2 So statement a is true the de nition tells us that ifz sin 1 y then it must be true that y sin x However statement b is false As an example to see when this is not true7 consider z 7139 Then y sin7r 07 but sin ly sin 1 0 07 and 0 31 7139 x In fact any number x that is outside the restricted domain 77r27 7T2 of y sinx that we used to de ne inverse sine will show that statement b is false7 exactly because these z cannot satisfy the second part of the de nition of inverse sine ls it true that if z tan 57 then 5 arctan x Solution the statement cannot possible be true 7717277172 For what values of x will sinarcsin s x The range of arctanz is 77r277r27 and 5 is not in this interval7 so In general7 arctantanx z only if z E a allx 0 F171 C l d 077T e none of the above Solution This statement is true for all z in the domain of arcsin x which is 717 1 Muss Lzrmm39 mm 5 HER mum so SHE Aw m mum Mus 0014 me To sum NEVEK nvsnr us ms I39VE WT Y Tans mass oer 5mm WT Bums ham your VIIDEIGMD m mmcmu mm or mm ARE WI39TNB MMquot msm smvmm MVTHWG DU39VEEVEI LEM BUT No Burs ms ISA MATTER oF LIFE AND MH 1 n yuanFlax apall you n nutK my um um mummy u 2 n w m up 9 n 25 um u um m m mm m g mm mm mm m IpId a la in an you 9 Wm yau xe um Ind mum a m u n m mm of a 2m mum 121an mr uptbt n quota zamlxr m up quotPm y wannad m m x mm a mp w o 10 m 4 X y x n rlpuxl nu ma mun yuu n m ngn mm 3 m a mm m u m my mm m u mm a Mptuxl m up mm m my m mm by a nun 9 um run on Lh nur pqm pm mu thruqu a building l35wng quotmu m 5 umquot I upquot u AxL am mm mm m n 5 1 lhbllq ltnl dear Wt mm m u m z nd my a m knal 1

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