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Math Help - Two trig question with squares and radians

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    Two trig question with squares and radians

    Ok, I know the Pythagorean identities but can't seem to solve these two question.

    Evaluate. Give exact anwser.
    sin² π/6 - tan² π/4 + cos² π/6

    so all I can do on this question so far is use the identity sin x + cos x= 1 to get to

    1 - tan² π/4

    then I am lost.



    The next question I have no idea what to do.

    Solve the following equation

    1 - 2 cos²Θ = -sinΘ, 0<Θ<2π
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    Quote Originally Posted by Apathy View Post
    Ok, I know the Pythagorean identities but can't seem to solve these two question.

    Evaluate. Give exact anwser.
    sin² π/6 - tan² π/4 + cos² π/6

    so all I can do on this question so far is use the identity sin x + cos x= 1 to get to

    1 - tan² π/4

    then I am lost.
    Hint: \tan\left(\frac{\pi}{4}\right) = 1
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    Quote Originally Posted by Apathy View Post
    The next question I have no idea what to do.

    Solve the following equation

    1 - 2 cos²Θ = -sinΘ, 0<Θ<2π
    This is the same as

    -(1-2\sin^2\theta)= -\sin\theta

    Make \sin\theta = a and solve as a quadratic.
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    Quote Originally Posted by pickslides View Post
    Hint: \tan\left(\frac{\pi}{4}\right) = 1
    Does that mean that tan π/4² will give me +1 because (-1)²=1?
    Will my awnser be 2?
    thank you!
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    Quote Originally Posted by pickslides View Post
    This is the same as

    -(1-2\sin^2\theta)= -\sin\theta

    Make \sin\theta = a and solve as a quadratic.
    Whoa! What identity was that? cos magically became sin!?

    i got to the point sinΘ=1/2 or sinΘ=-1. Now do I reject -1 because because 0<Θ<2π or am I missing something? Also, how do I get rid of the sin?

    I realize this stuff is elementary but I feel that my teacher gave an insufficient explanation for the trig unit.
    Last edited by Apathy; January 23rd 2010 at 05:39 PM.
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    Quote Originally Posted by Apathy View Post
    Does that mean that tan π/4² will give me +1 because (-1)²=1?
    Will my awnser be 2?
    thank you!
    It's 1 not -1. (1)^2 = 1. And so you have 1 - 1 = 0, not 2. You need to take more care with basic arithmetic.

    Quote Originally Posted by Apathy View Post
    Whoa! What identity was that cos magically became sin!?
    The left hand side of the equation you posted has been converted into -1 + 2 \sin^2 \theta using the Pythagorean Identity. Now you're are expected to re-arrange the resulting equation into a quadratic equation. Look in your class notes or textbook for a similar example.

    Please show all your work if you need more help.
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    Quote Originally Posted by mr fantastic View Post
    It's 1 not -1. (1)^2 = 1. And so you have 1 - 1 = 0, not 2. You need to take more care with basic arithmetic.


    The left hand side of the equation you posted has been converted into -1 + 2 \sin^2 \theta using the Pythagorean Identity. Now you're are expected to re-arrange the resulting equation into a quadratic equation. Look in your class notes or textbook for a similar example.

    Please show all your work if you need more help.
    Thank you. I was under the impression 1-tan² π/4 meant that when I used the identity that the I would include the negative sign but then I realized that the negative is not part of the identity so your way does make perfect sense. (sorry for that rant, I am not even sure that was coherent).



    Here is all my work for the second question. Still can't find the answer... maybe math isn't my forte

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    Quote Originally Posted by Apathy View Post

    Here is all my work for the second question. Still can't find the answer... maybe math isn't my forte

    \sin(\theta)= \frac{1}{2}\implies \theta =\frac{\pi}{6}

     \sin(\theta)= -1\implies \theta =\frac{3\pi}{2}

    There are some more answers to find given your domain.

    I think you will do just fine with a little bit of hard work and dedication.
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