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anonymous

  • one year ago

Find the exact value of tan inverse

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  1. anonymous
    • one year ago
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  2. UnkleRhaukus
    • one year ago
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    tan theta = opp / adj

  3. UnkleRhaukus
    • one year ago
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    (there is no inverse)

  4. anonymous
    • one year ago
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    this is a dumb question.. but what does the theta sign look like?

  5. UnkleRhaukus
    • one year ago
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    theta : \(\theta\)

  6. anonymous
    • one year ago
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    that's the sign I used but I thought it meant inverse :0

  7. UnkleRhaukus
    • one year ago
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    \[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\]\[\Downarrow\]\[\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)=\arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right)\]

  8. UnkleRhaukus
    • one year ago
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    the question is only asking you to find \(\tan\theta\), you don't have to compute the value of theta,

  9. anonymous
    • one year ago
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    It's saying the equation has too many equal signs

  10. UnkleRhaukus
    • one year ago
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    what is the length of the side opposite to theta in the diagram?

  11. anonymous
    • one year ago
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    is 6 the opp and 2 and 5 the adj?

  12. UnkleRhaukus
    • one year ago
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    yes, opp = 6 and adj = 2√5

  13. anonymous
    • one year ago
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    my calculator said it was 1/2 as the answer, but it said that 1/2 is not correct

  14. UnkleRhaukus
    • one year ago
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    \(\tan\theta = \dfrac{6}{2\sqrt 5}\)

  15. UnkleRhaukus
    • one year ago
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    now cancel the common factor

  16. anonymous
    • one year ago
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    what's the common factor?

  17. UnkleRhaukus
    • one year ago
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    \[\tan\theta = \dfrac{6}{2\sqrt 5}=\dfrac{2\times3}{2\times\sqrt 5}=\]

  18. anonymous
    • one year ago
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    \[\tan \emptyset \frac{ 6}{ 5 }=\frac{ 3 }{ 5 }\]

  19. UnkleRhaukus
    • one year ago
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    now rationalize the denominator \[\tan\theta = \frac{6}{2\sqrt 5}=\frac{3}{\sqrt 5}=\frac{3}{\sqrt 5}\times\frac{\sqrt5}{\sqrt5}=\]

  20. anonymous
    • one year ago
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    20..?

  21. UnkleRhaukus
    • one year ago
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    \[\frac{3}{\sqrt 5}\times\frac{\sqrt5}{\sqrt5}=\frac{3\times\sqrt5}{\sqrt5\times\sqrt5}\] now simplify the denominator

  22. anonymous
    • one year ago
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    would it be 1 because 5 can go into 5 once?

  23. UnkleRhaukus
    • one year ago
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    \[\sqrt5\sqrt5=\sqrt5^2= .....\]

  24. anonymous
    • one year ago
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    i'm not even sure how to go about that :o

  25. UnkleRhaukus
    • one year ago
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    \[√x^2 = x\]

  26. anonymous
    • one year ago
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    oh gosh

  27. UnkleRhaukus
    • one year ago
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    ikr

  28. anonymous
    • one year ago
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  29. anonymous
    • one year ago
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    my options don't even make sense then

  30. UnkleRhaukus
    • one year ago
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    we are very close to one of those

  31. UnkleRhaukus
    • one year ago
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    what is the square root of five squared?

  32. anonymous
    • one year ago
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    5? I think

  33. anonymous
    • one year ago
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    oh wait i did that wrong

  34. UnkleRhaukus
    • one year ago
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    yes, so what is our final answer?

  35. anonymous
    • one year ago
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    5 squared over

  36. anonymous
    • one year ago
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    3 I wanna say

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