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anonymous

  • 5 years ago

simple trig identities problem! Solve the following quadratic trig equations algebraically (without graphing technology) for the domain 0o < x < 360o. Use exact solutions whenever possible. a) 6cos^2(theta ) + cos(theta ) - 1 = 0 b) 2 - 2sin^2( theta) = cos(theta )

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  1. anonymous
    • 5 years ago
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    put cos(theta) = x in the first equation and solve for x, and then substitute it back into cos theta

  2. anonymous
    • 5 years ago
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    for the second one 2-2sin^theta = 2(1-sin^2theta) = 2 cos^2theta and then put cos theta = x and solve for x

  3. anonymous
    • 5 years ago
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    i'm sorry but i don't understand any of that...

  4. anonymous
    • 5 years ago
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    substitute cos theta = x in the first problem and post what you got.

  5. anonymous
    • 5 years ago
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    as in.. 6x^2+x-1?? like a quadratic?

  6. anonymous
    • 5 years ago
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    yes.

  7. anonymous
    • 5 years ago
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    so solve that quadratic equation.

  8. anonymous
    • 5 years ago
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    i dont remember how to when the x^2 value has a coefficient..

  9. anonymous
    • 5 years ago
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    Find out and solve it. If you have done it before, I am sure you can solve it.

  10. anonymous
    • 5 years ago
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    http://www.youtube.com/watch?v=1Pva-Iv43Nc

  11. anonymous
    • 5 years ago
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    well everything becomes a fraction if i factor out the 6.... that vid didnt help.

  12. anonymous
    • 5 years ago
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    6x2+x-1 = 6x2+3x-2x-1

  13. anonymous
    • 5 years ago
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    alright, so now what is the next step?

  14. anonymous
    • 5 years ago
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    do you know how to factor quadratic equations?

  15. anonymous
    • 5 years ago
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    using the qudratic frmula? yes. why did i need to break up that middle term?

  16. anonymous
    • 5 years ago
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    okay. there is another way to solve quadratic eqns. its called factoring. so 6x2+3x-2x-1 = 3x(2x+1)-1(2x+1) = (3x-1)(2x+1)=0. so x = 1/3 or x = -1/2.

  17. anonymous
    • 5 years ago
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    ok, but how does this relate to the trig question? haha

  18. anonymous
    • 5 years ago
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    so if x = 1/3, it means cos theta = 1/3. and x= -1/2. so cos theta = -1/2. solve foe theta within 0 and 360 degrees

  19. anonymous
    • 5 years ago
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    wwhat do you mean by solving for theta between 0 and 360? sorry i'm so bad at this!

  20. anonymous
    • 5 years ago
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    just find theta.

  21. anonymous
    • 5 years ago
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    dont worry about the 0 and 360.

  22. anonymous
    • 5 years ago
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    post the values of theta you got.

  23. anonymous
    • 5 years ago
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    arent the x= values the solutions?

  24. anonymous
    • 5 years ago
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    No, x is just a variable you used to denote cos theta. so you have to find theta

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