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greysmither

  • 2 years ago

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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  1. ash2326
    • 2 years ago
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    @greysmither what's tan 45?

  2. Avva
    • 2 years ago
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    it is 135 degree ,, Aren't u allowed to use calculator??

  3. ash2326
    • 2 years ago
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    Avva 135 is just one of the answer, it has several answers

  4. amistre64
    • 2 years ago
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    tan-1 only has one answer :)

  5. ash2326
    • 2 years ago
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    @amistre64 tan (theta)=-1 will have several solutions

  6. amistre64
    • 2 years ago
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    yep

  7. Avva
    • 2 years ago
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    yup you can add 180 degrees and you'll figure out that 135 n 315 both have tan of -1

  8. ash2326
    • 2 years ago
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    \[\tan \theta=-1\] so \[\theta = n\pi +3\frac{\pi}{4}\] n=0, 1, 2, 3 and so on

  9. greysmither
    • 2 years ago
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    So this pretty much a unit circle-dependent problem?

  10. greysmither
    • 2 years ago
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    this is*

  11. ash2326
    • 2 years ago
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    Yeah:)

  12. greysmither
    • 2 years ago
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    Could it also be \[7\pi/4 + \pi n\]?

  13. greysmither
    • 2 years ago
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    since both of those quadrants create -1?

  14. ash2326
    • 2 years ago
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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

  15. greysmither
    • 2 years ago
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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?

  16. greysmither
    • 2 years ago
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    So confusing :(

  17. ash2326
    • 2 years ago
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    Sorry, Just wait for some time, I'll help you:)

  18. ash2326
    • 2 years ago
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    Sorry kept you waiting:(

  19. greysmither
    • 2 years ago
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    Its okay I really appreciate your help

  20. ash2326
    • 2 years ago
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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

  21. greysmither
    • 2 years ago
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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 ;)

  22. ash2326
    • 2 years ago
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    Thanks Greysmither , this is the answer:)

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