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anonymous

  • one year ago

Solving Trigonometric Equations

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  1. freckles
    • one year ago
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    post the equation when you are ready :)

  2. anonymous
    • one year ago
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    |dw:1436825812888:dw|

  3. freckles
    • one year ago
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    write in terms of just cos by using Pythagorean identity

  4. anonymous
    • one year ago
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    whats that?

  5. freckles
    • one year ago
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    you will have a quadratic equation in terms of cos(theta)

  6. freckles
    • one year ago
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    \[\sin^2(\theta)+\cos^2(\theta)=1 \text{ is one of the pythagorean identities }\]

  7. freckles
    • one year ago
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    \[\sin^2(\theta)=1-\cos^2(\theta)\]

  8. freckles
    • one year ago
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    \[3(1-\cos^2(\theta))=1+\cos(\theta) \\ 3-3\cos^2(\theta)=1+\cos(\theta)\]

  9. freckles
    • one year ago
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    if you want replace cos(theta) with u for now \[3-3u^2=1+u\] solve for u

  10. freckles
    • one year ago
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    by first putting everything on one side

  11. anonymous
    • one year ago
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    but i have a range to follow

  12. anonymous
    • one year ago
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    and i got u=1

  13. freckles
    • one year ago
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    hmmm how did you get u=1?

  14. freckles
    • one year ago
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    \[3-3u^2=1+u \\ \text{ add } 3u^2 \text{ and subtract } 3 \text{ on both sides } \\ 0=3u^2+u+1-3 \\ 0=3u^2+u-2 \\ 0=(3u-2)(u+1)\]

  15. freckles
    • one year ago
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    neither u+1=0 or 3u-2=0 leads to u=1

  16. freckles
    • one year ago
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    but anyways you have the following equations to solve recall we replaced cos(theta) with u so we actually have \[\cos(\theta)+1=0 \text{ or } 3\cos(\theta)-2=0 \] you need to solve these two equations for theta

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