greysmither
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 <_>
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ash2326
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@greysmither what's tan 45?
Avva
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it is 135 degree ,, Aren't u allowed to use calculator??
ash2326
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Avva 135 is just one of the answer, it has several answers
amistre64
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tan-1 only has one answer :)
ash2326
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@amistre64 tan (theta)=-1 will have several solutions
amistre64
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yep
Avva
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yup you can add 180 degrees and you'll figure out that 135 n 315 both have tan of -1
ash2326
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\[\tan \theta=-1\]
so
\[\theta = n\pi +3\frac{\pi}{4}\]
n=0, 1, 2, 3 and so on
greysmither
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So this pretty much a unit circle-dependent problem?
greysmither
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this is*
ash2326
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Yeah:)
greysmither
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Could it also be \[7\pi/4 + \pi n\]?
greysmither
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since both of those quadrants create -1?
ash2326
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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
greysmither
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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?
greysmither
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So confusing :(
ash2326
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Sorry, Just wait for some time, I'll help you:)
ash2326
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Sorry kept you waiting:(
greysmither
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Its okay I really appreciate your help
ash2326
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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
greysmither
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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
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Thanks Greysmither , this is the answer:)