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anonymous

  • one year ago

Use a graphing calculator to solve the equation 3tan 1/3 0=8 in the interval from 0 to 2pi Round your answers to the nearest hundredth.

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  1. jim_thompson5910
    • one year ago
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    This equation? \[\Large 3\tan\left(\frac{1}{3}\theta\right) = 8\]

  2. anonymous
    • one year ago
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    yes

  3. jim_thompson5910
    • one year ago
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    ok replace theta with x \[\Large 3\tan\left(\frac{1}{3}\theta\right) = 8\] \[\Large 3\tan\left(\frac{1}{3}x\right) = 8\]

  4. jim_thompson5910
    • one year ago
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    then subtract 8 from both sides \[\Large 3\tan\left(\frac{1}{3}x\right) = 8\] \[\Large 3\tan\left(\frac{1}{3}x\right)-8 = 8-8\] \[\Large 3\tan\left(\frac{1}{3}x\right)-8 = 0\]

  5. jim_thompson5910
    • one year ago
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    now graph `y = 3*tan(1/3x)-8` into a graphing calculator here's a free one to use if you don't have a graphing calculator https://www.desmos.com/calculator

  6. jim_thompson5910
    • one year ago
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    look for the point where the graph crosses the x axis

  7. anonymous
    • one year ago
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  8. anonymous
    • one year ago
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    this is what i am given

  9. jim_thompson5910
    • one year ago
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    what did you type in?

  10. anonymous
    • one year ago
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    y=3*tan (1/3x)-8

  11. jim_thompson5910
    • one year ago
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    strange, I'm getting this (see attached image)

  12. campbell_st
    • one year ago
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    if you are being asked to solve, why not graph y = 8 and \[y = \tan(\frac{x}{3})\] and find the points of intersection in the given domain.

  13. jim_thompson5910
    • one year ago
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    @campbell_st it should be `3tan(x/3)`

  14. jim_thompson5910
    • one year ago
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    but that's a good alternative

  15. anonymous
    • one year ago
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    that is weird mine will not give me that graph. so approx -5.9 and 3.7

  16. jim_thompson5910
    • one year ago
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    https://www.desmos.com/calculator/fgkktgo5bo

  17. jim_thompson5910
    • one year ago
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    focus on the interval from 0 to 2pi 2pi = 6.28 so you're only focusing on roots between 0 and 6.28

  18. anonymous
    • one year ago
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    3.64 is the only point located between the two so that would be the answer

  19. jim_thompson5910
    • one year ago
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  20. jim_thompson5910
    • one year ago
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    3.64 is correct

  21. anonymous
    • one year ago
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    Thank you again for explaining!

  22. jim_thompson5910
    • one year ago
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    sure thing

  23. campbell_st
    • one year ago
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