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bii17 Group Title

If an angle theta increases uniformly, find the smallest positive value of theta for which tan theta increases 8 times as fast as sin theta

  • 2 years ago
  • 2 years ago

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  1. wio Group Title
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    Would it be something like this? \[\Large \frac{d}{d\theta}tan(\theta) =8\cdot \frac{d}{d\theta}sin(\theta) \] Where \[\Large \frac{d}{d\theta}tan(\theta) > 0\] What is the topic of the curriculum?

    • 2 years ago
  2. bii17 Group Title
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    Diffrentiation with respect to time.. @wio

    • 2 years ago
  3. wio Group Title
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    So do you think you can find those derivatives, and then solve for \(\theta\)?

    • 2 years ago
  4. bii17 Group Title
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    \[\sec^2 \theta =8 \cos \theta]

    • 2 years ago
  5. bii17 Group Title
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    \[\sec^2 \theta =8 \cos \theta\]

    • 2 years ago
  6. wio Group Title
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    Now, what is \(\sec^2(\theta )\) in terms of \(\sin(\theta) \) and \(\cos(\theta)\)?

    • 2 years ago
  7. bii17 Group Title
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    i know is sec = 1/ cos

    • 2 years ago
  8. wio Group Title
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    Do you still need help solving for \(\theta\)?

    • 2 years ago
  9. bii17 Group Title
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    yes..

    • 2 years ago
  10. wio Group Title
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    Ok so we have \[\Large \frac{1}{\cos^2(\theta)} = 8\cdot \cos(\theta)\]How can we isolate \(\theta \) further?

    • 2 years ago
  11. bii17 Group Title
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    what will happen next?? no idea. -_-

    • 2 years ago
  12. wio Group Title
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    How about we multiply both sides by \(\cos^2(\theta)\)? Try that.

    • 2 years ago
  13. bii17 Group Title
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    then it will become 1= 8 cos^3 theta ??

    • 2 years ago
  14. wio Group Title
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    Yes! So what about getting rid of the coefficient?

    • 2 years ago
  15. bii17 Group Title
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    1/8 = cos ^3 theta ??

    • 2 years ago
  16. wio Group Title
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    Now it's just algebra. We learned that long ago.

    • 2 years ago
  17. wio Group Title
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    How do you get rid of an exponent?

    • 2 years ago
  18. bii17 Group Title
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    hmm i dont know can u help about it?

    • 2 years ago
  19. wio Group Title
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    Why don't you take the cubed root of both sides?

    • 2 years ago
  20. bii17 Group Title
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    oww okay I get it :) THanks

    • 2 years ago
  21. wio Group Title
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    Just remember that you want the smallest positive \(\theta \), and that \(\cos(\theta)\) must also be positive since they should be increasing.

    • 2 years ago
  22. wio Group Title
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    Otherwise there would be many solutions!

    • 2 years ago
  23. bii17 Group Title
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    I get theta = 60 is that correct?

    • 2 years ago
  24. bii17 Group Title
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    @wio

    • 2 years ago
  25. wio Group Title
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    Yes! http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/300px-Unit_circle_angles_color.svg.png

    • 2 years ago
  26. bii17 Group Title
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    Thank you :)

    • 2 years ago
  27. hartnn Group Title
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    Great explanation @wio :)

    • 2 years ago
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