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Babynini

  • one year ago

Solve the given equation tan^2(theta)-2sec(theta)=2

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  1. Babynini
    • one year ago
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    @freckles I love you <3 just so you know xD I've gotten to sec(theta)=-1/2 and sec(theta)=1

  2. Babynini
    • one year ago
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    But on the unit circle secant never = -1/2 and it equals 1 at 0

  3. Babynini
    • one year ago
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    @peachpi :)?

  4. anonymous
    • one year ago
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    Pi and -pi work, but they're certainly not the only answers. Positive and negative 1.231, 5.052, and 7.514 work as well.

  5. Babynini
    • one year ago
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    how did you get those?

  6. Babynini
    • one year ago
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    does pi(n) where n is an interger work?

  7. anonymous
    • one year ago
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    tan² x -2 sec x = 2 sec² x - 1 -2 sec x = 2 sec²x - 2 sec x - 3 = 0 (sec x - 3)(sec x + 1) = 0 sec x = 3, sec x = -1

  8. Babynini
    • one year ago
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    ooh crud. I added two instead of subtracting it

  9. Babynini
    • one year ago
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    oh wow I messed up all over the place.

  10. Babynini
    • one year ago
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    what did you do with the 2secx?

  11. Babynini
    • one year ago
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    oh I see 2secx-sec^2x-2 = 0

  12. anonymous
    • one year ago
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    I factored. and you have them reversed in the equation you just wrote

  13. Babynini
    • one year ago
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    What's the correct way?

  14. anonymous
    • one year ago
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    sec²x - 2 sec x - 3 = 0

  15. Babynini
    • one year ago
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    ah right. so but secant never = 3 on the unit circle..

  16. Babynini
    • one year ago
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    and = -1 and pi

  17. anonymous
    • one year ago
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    yes, pi is a solution. For sec x = 3, the solution is x = arcsec 3

  18. Babynini
    • one year ago
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    ah k. So for me with my little scientific calculator how do I do arc sec 3

  19. Babynini
    • one year ago
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    sec = 1/cos but with the inverse I want to be careful o.o

  20. anonymous
    • one year ago
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    sec x = 3 cos x = 1/3 x = arccos (1/3)

  21. Babynini
    • one year ago
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    oh! :)

  22. anonymous
    • one year ago
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    that'll give you an angle in the 1st quadrant. Subtract it from 360 to get the angle in the 4th quadrant.

  23. anonymous
    • one year ago
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    or rather 2pi

  24. Babynini
    • one year ago
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    does it work to add two pi to that? or just subtracting it from 2pi?

  25. Babynini
    • one year ago
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    the answers they give are kpi = we have this one! 0.72+2kpi = we don't have this. 5.56+2kpi = and we dont' have this either.

  26. anonymous
    • one year ago
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    adding 2pi just gives the same angle you already found. Subtracting x from 2pi gives the angle in the 4th quad. Where did these answers come from?

  27. Babynini
    • one year ago
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    aah I see the answer part of the book I'm doing the odd problems in my textbook which gives the answers in the back.

  28. Babynini
    • one year ago
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    oh crap. Just a moment.

  29. anonymous
    • one year ago
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    I'm getting 5.05 and 1.23

  30. Babynini
    • one year ago
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    Sorry, yeah. I was looking at 7 instead of 5. the answers are (2k+1)pi, 1.23+2kpi, 5.05+2kpi

  31. anonymous
    • one year ago
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    ok. you know how to get those?

  32. Babynini
    • one year ago
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    um 1.23, 5.05 came from theta = arcos(1/3) and pi came from sec(theta)=-1

  33. Babynini
    • one year ago
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    and I understand the adding 2pi(k)

  34. Babynini
    • one year ago
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    I'm not sure why the pi one is written as (2k+1)pi ?

  35. anonymous
    • one year ago
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    That's the same as π+2πk. They factored the pi out

  36. Babynini
    • one year ago
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    ah ok I see.

  37. Babynini
    • one year ago
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    haha I told myself I would keep doing these until I get the answer entirely on my own..but going like this it seems that won't be anytime soon =.= K, this one makes sense now though :)

  38. anonymous
    • one year ago
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    ok great. Maybe take a break if you don't have a deadline. These definitely take time to get used to

  39. Babynini
    • one year ago
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    Final on Friday..hah but I may move onto studying another part.

  40. anonymous
    • one year ago
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    ah.. I don't envy you. good luck

  41. Babynini
    • one year ago
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    yeah xD thanks.

  42. Babynini
    • one year ago
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    Precalc 2 man. phew.

  43. Babynini
    • one year ago
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    For you it's probably no biggy xP

  44. anonymous
    • one year ago
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    yeah give it a few years, you'll either never use it, or wonder how you lived without knowing it. There's no in-between

  45. Babynini
    • one year ago
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    I fear it may be the latter D: Just because i despise it so much, i'm bound to end up being a math major lol

  46. Babynini
    • one year ago
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    Welp, moving onto question next. Thanks for all your help :)

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