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anonymous

  • one year ago

Find the exact value by using a half-angle identity. \[\tan \left( \frac{ 7\pi }{8 } \right)\]

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  1. anonymous
    • one year ago
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    |dw:1438036308621:dw|

  2. Loser66
    • one year ago
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    yes

  3. anonymous
    • one year ago
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    I'm kinda lost with solving it.

  4. anonymous
    • one year ago
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    Hang on, I will put my work.

  5. Loser66
    • one year ago
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    why?

  6. anonymous
    • one year ago
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    \[\tan \frac{ \frac{ 7\pi }{ 4 } }{ 2 }=\frac{ 1-\cos \frac{ 7\pi }{ 4 } }{ \sin \frac{ 7\pi }{ 4 } }\]

  7. welshfella
    • one year ago
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    you can use tan (x /2) = sin x / (1 = cos x)

  8. welshfella
    • one year ago
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    * (1 + cos x)

  9. anonymous
    • one year ago
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    \[=\frac{ 1-\frac{ \sqrt{2} }{ 2 } }{ \frac{ -\sqrt{2} }{ 2 } }\]

  10. Loser66
    • one year ago
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    yes

  11. Loser66
    • one year ago
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    simplify more to get 1-sqrt2

  12. anonymous
    • one year ago
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    Is the numerator already simplified? Or can I use 2/2 instead of 1?

  13. Loser66
    • one year ago
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    |dw:1438036640856:dw|

  14. Loser66
    • one year ago
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    |dw:1438036676374:dw|

  15. Loser66
    • one year ago
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    ok?

  16. anonymous
    • one year ago
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    Ohhhh! Thank you! Now I get it. :)

  17. anonymous
    • one year ago
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    The answer is: \[1-\sqrt{2}\] right?

  18. Loser66
    • one year ago
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    yup

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spraguer (Moderator)
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