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Denebel

  • 4 years ago

How do I solve 8cos x = (sec x)^2?

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  1. ksmith197
    • 4 years ago
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    sec^2x = 1/cos^2x

  2. ksmith197
    • 4 years ago
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    8cos^3x=0

  3. ksmith197
    • 4 years ago
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    cos(pi/2) = 0

  4. ksmith197
    • 4 years ago
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    so 8cos^3(pi/2)=0

  5. Denebel
    • 4 years ago
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    I got lost on the first step.. Sorry, can you explain it more?

  6. ksmith197
    • 4 years ago
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    sure, first you need to memorize all of the identitites memorize : sec(x) = 1/cos(x)

  7. Jemurray3
    • 4 years ago
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    whoa whoa whoa, \[8\cos^2(x) = 1\] not zero...

  8. ksmith197
    • 4 years ago
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    so sec^2(x) = 1/cos^2(x)

  9. ksmith197
    • 4 years ago
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    ah right 1 my bad

  10. Denebel
    • 4 years ago
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    |dw:1329118155688:dw| So like this?

  11. ksmith197
    • 4 years ago
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    anyway multiply across so 1/cos^2(x) * cos^2(x) = cos^2(x) * 8cos(x)

  12. ksmith197
    • 4 years ago
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    1 = 8cos^3(x)

  13. Denebel
    • 4 years ago
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    Ohh I see. Thank you.

  14. Denebel
    • 4 years ago
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    So it would be x = pi/3 instead of pi/2 right?

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