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gjhfdfg

  • 3 years ago

Rewrite the expression as a trigonometric function of a single angle measure.

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  1. gjhfdfg
    • 3 years ago
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    \[\frac{ \tan4 \theta + \tan 2 \theta }{ 1 - \tan 4 \theta + \tan 2 \theta }\]

  2. hsmt
    • 3 years ago
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    hi. do you still need help with this one?

  3. gjhfdfg
    • 3 years ago
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    Yes, I'm so lost on how to solve it

  4. hsmt
    • 3 years ago
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    do you know the tangent addition formula?

  5. hsmt
    • 3 years ago
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    tan(a+b)=(tan a +tan b)/(1-tan a tanb)

  6. hsmt
    • 3 years ago
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    have you seen this formula before?

  7. hsmt
    • 3 years ago
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    now think about the angle a=4theta and the angle b=2theta. does this help?

  8. gjhfdfg
    • 3 years ago
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    Ive seen it but never used it,

  9. hsmt
    • 3 years ago
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    ah. well, your teacher is giving you the opportunity here

  10. gjhfdfg
    • 3 years ago
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    I'm confused on how I solve it with the this formula using the 'theta'

  11. hsmt
    • 3 years ago
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    ok. well, it is more recognition than solving. look at the form of the equation i gave you and the relation you wrote above. write this puppy as the tangent of the sum of the two angles you have been given (4theta and 2theta)

  12. hsmt
    • 3 years ago
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    it is good to ask questions if you are in doubt. :)

  13. gjhfdfg
    • 3 years ago
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    Sorry, If it takes to long to respond, I'm still confused a little so I'm trying to write it down so that would hopefully help me get it

  14. hsmt
    • 3 years ago
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    no problem. so the form of the equation is tan (a+b)=(tan a +tan b)/(1-tan a tan b). substitute for a 4theta and for b 2theta

  15. gjhfdfg
    • 3 years ago
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    So, tan 4theta + tan 2theta / 1- tan 4theta * tan 2.?

  16. hsmt
    • 3 years ago
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    we are interested in the left side. the tan (a+b) part. this condenses the mess you were given.

  17. gjhfdfg
    • 3 years ago
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    So 4 theta + 2 theta.?

  18. hsmt
    • 3 years ago
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    which becomes tan ?

  19. gjhfdfg
    • 3 years ago
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    You would add the 4 & 2 together & get 6 & 6 would be the tan wouldn't it.?

  20. hsmt
    • 3 years ago
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    perfect. yes!! so you tan 6theta, which is the trig function (tan) of a single angle 6theta.

  21. gjhfdfg
    • 3 years ago
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    Alright thank you for help.! :-) I understand this now.!

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