Question

Practice Problems for the Final (already!) EGG-Zact Answers Only. For these questions you are to state the exact answers only. If you even think about writing down a decimal, the earth willl crack open and zombies will be released to devour your calculator. a) Find all solutions using radians. You should have two formulas that represent the solutions to this equation. Each formula will involve the arccosine function added or subtracted with some multiple of T. I could be a nag and ask you to write down the egg zact answer, but that would be kinda rude. -3 cos(40)-2=0 b) Find the first two positive solutions. State the exact answers solving by hand using the inverse sine function. (Watch out for the zombies). 4 sin(6x) -1

Answer 1

Mathematics June 13, 2019 Sabyasachi Solution (a) - 3 cos(40) - 2 0 - 3 cos(40) 2 2 COs(40) = 3 Cos(40) =-COS arccos cos cos( -x cos(40 T arcCoS COS 40 2nT t cos y r= 2n7 ± y cos arccos 40=3nr or 40 nT arccos arccos 3 1 1 1 n EZ =nn arccos or arccos (b) 4 sin(6)-1 1 sin(6x) = 4 () () () sin(6)= - sin arcsin -sin cos (-) > sin(6a): arcsin sin 6 nT(-1)" arcsin 6x nT+(-1)" arcsin () + (-1)n+1 arcsin = nT1)0.25268| , n e Z F.' arcsin = 0.25268) 6 So, the first two positive solutions coresponds to n 1,2. For n 1, (T0.2526802) 0.565712 and For n (27 - 0.25268) = 1.005084. 2, Therefore 0.565712, 1.005084