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Anikate

  • one year ago

how do u do this? cos2θ+cosθ=0 find solutions

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  1. Anikate
    • one year ago
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    |dw:1434351527647:dw|

  2. ganeshie8
    • one year ago
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    As a start, factor out \(\large \cos\theta\)

  3. Anikate
    • one year ago
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    ok

  4. Anikate
    • one year ago
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    |dw:1434351738430:dw|

  5. Anikate
    • one year ago
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    @ganeshie8

  6. ganeshie8
    • one year ago
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    Ahh that is wrong, and don't wry thats a typical mistake committed by everyone in the start

  7. Anikate
    • one year ago
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    hmm lol

  8. ganeshie8
    • one year ago
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    \(\large \cos^2\theta\) is same as \(\large (\cos \theta)^2\)

  9. Anikate
    • one year ago
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    ok

  10. Anikate
    • one year ago
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    lol idk how that helps

  11. ganeshie8
    • one year ago
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    when you factor out \(\cos\theta\) from \((\cos\theta)^2\), there will be \(\cos\theta\) left behind : |dw:1434352204156:dw|

  12. Anikate
    • one year ago
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    oooh

  13. ganeshie8
    • one year ago
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    next use zero product property if the product of two factors is 0, then at least one of the factors must be 0

  14. Anikate
    • one year ago
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    ok so the cos theta on the outside is = to 0

  15. ganeshie8
    • one year ago
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    |dw:1434352435421:dw|

  16. Anikate
    • one year ago
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    thats it?

  17. ganeshie8
    • one year ago
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    we need to find \(\theta\) using unit circle

  18. ganeshie8
    • one year ago
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    for what values of \(\theta\), the cos function becomes 0 ?

  19. Anikate
    • one year ago
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    umm...... 0 degrees?

  20. ganeshie8
    • one year ago
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    careful, do u have unit circle ?

  21. Anikate
    • one year ago
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    in google images yes

  22. Anikate
    • one year ago
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    lol

  23. ganeshie8
    • one year ago
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    Good

  24. ganeshie8
    • one year ago
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    The first coordinate represents the cosine value : |dw:1434352712518:dw|

  25. Anikate
    • one year ago
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    oh 1,0

  26. ganeshie8
    • one year ago
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    No, listen to my question again. For what values of \(\theta\), the cosine function is 0 ?

  27. Anikate
    • one year ago
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    hey is 3:20am here, I can barely concentrate, can u please leave the work, and I'll check back in the morning? sorry and thanks for all ur help and co operation! :)

  28. ganeshie8
    • one year ago
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    Assuming we want to find the principle value, from the unit circle, \[\cos\theta = 0 \implies \theta = 90,270\] \[\cos\theta = -1 \implies \theta = 180\]

  29. ganeshie8
    • one year ago
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    so \(\theta = 90,180,270\) are the solutions

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