anonymous
  • anonymous
I'm trying to solve this but I honestly have no idea how to move forward. All I have done so far is this: theta=tan^-1(-1) Now I'm stuck<_>
Mathematics
jamiebookeater
  • jamiebookeater
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jamiebookeater
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ash2326
  • ash2326
@greysmither what's tan 45?
anonymous
  • anonymous
it is 135 degree ,, Aren't u allowed to use calculator??
ash2326
  • ash2326
Avva 135 is just one of the answer, it has several answers

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amistre64
  • amistre64
tan-1 only has one answer :)
ash2326
  • ash2326
@amistre64 tan (theta)=-1 will have several solutions
amistre64
  • amistre64
yep
anonymous
  • anonymous
yup you can add 180 degrees and you'll figure out that 135 n 315 both have tan of -1
ash2326
  • ash2326
\[\tan \theta=-1\] so \[\theta = n\pi +3\frac{\pi}{4}\] n=0, 1, 2, 3 and so on
anonymous
  • anonymous
So this pretty much a unit circle-dependent problem?
anonymous
  • anonymous
this is*
ash2326
  • ash2326
Yeah:)
anonymous
  • anonymous
Could it also be \[7\pi/4 + \pi n\]?
anonymous
  • anonymous
since both of those quadrants create -1?
ash2326
  • ash2326
Yeah it should be \[ n\pi \pm \pi/4\] n=1,2 ,3 and so on I missed that, it'd include \(7\pi/4 + n\pi\) also
anonymous
  • anonymous
I thought that you couldn't include pi/4 and 5pi/4 in quadrants 1 and 3 because they equal 1 when I'm looking for -1?
anonymous
  • anonymous
So confusing :(
ash2326
  • ash2326
Sorry, Just wait for some time, I'll help you:)
ash2326
  • ash2326
Sorry kept you waiting:(
anonymous
  • anonymous
Its okay I really appreciate your help
ash2326
  • ash2326
We have \[\tan x=-1\] so x is eithere 3pi/4 , 7pi/4 and so on \[x= n\pi -\pi/4\] if n=1 x=3 pi/4 n=2 x= 7 pi/4 so this will include all possible solutions. This is your answer
anonymous
  • anonymous
So, just to clarify \[x=-\pi/4+n \pi\] is the final answer. I can't thank you enough!! I wish I could give you 100 medals ;)
ash2326
  • ash2326
Thanks Greysmither , this is the answer:)

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