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Math Help - Trig

  1. #1
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    Trig

    Can someone help me with these?

    1. Simplify, listing reasons: cos^2 theta times csc theta + sin theta.

    2. Given the stated information, sketch theta and find the exact values.
    a. cos alpha(in degrees) = -1\2, 180 degrees < alpha < 360 degrees, find alpha, sin value and tan value.
    b. If sin^-1 (squareroot of 3 over 2) = alpha^R ad alpha^R lies in quadrant II, find alpha^R, cos value and tan value.
    c. tan alpha^R = -1/root3, pi < alpha < 2pi, find alpha, sex value, and csc value
    d. sin alpha(in degrees) = 0, 90 degrees < or = to alpha < or = to 270 degrees, find alpha, cos value and tan value.
    e. sec alpha^R = root 2, pi < alpha < 2pi, find alpha, cot value and sin value
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jakej78 View Post
    Can someone help me with these?
    Sure, we can help. What have you tried, and where do you get stuck?
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  3. #3
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    The first one, I don't even know where to start, considering I wasn't taught it, but was still given it.

    The second one, I don't know how to start it, nor how to graph it. I just honestly don't get it, and I don't think I was taught it quite yet.. For a, I'm guessing you graph -1/2 (how though?) and I don't know what the 180 < alpha < 360 is?
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jakej78 View Post
    The first one, I don't even know where to start, considering I wasn't taught it, but was still given it.

    The second one, I don't know how to start it, nor how to graph it. I just honestly don't get it, and I don't think I was taught it quite yet.. For a, I'm guessing you graph -1/2 (how though?) and I don't know what the 180 < alpha < 360 is?
    a) \cos\alpha=-\frac{1}{2} means we are dealing with an angle in either QII or QIII. Then \alpha=\arccos(\frac{1}{2})=60^{\circ} implies that \alpha=120^{\circ},240^{\circ} for \alpha\in[0,360^{\circ}]. But, we want \alpha\in(180^{\circ},360^{\circ}). Therefore, \alpha=240^{\circ}
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  5. #5
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    Ohhh okay, I get that now.. makes such more sense!

    I'm having trouble with
    1. Simplify, listing reasons: cos^2 theta times csc theta + sin theta.
    b. If sin^-1 (squareroot of 3 over 2) = alpha^R and alpha^R lies in quadrant II, find alpha^R, cos value and tan value.

    Can you help me with those?
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jakej78 View Post
    Ohhh okay, I get that now.. makes such more sense!

    I'm having trouble with
    1. Simplify, listing reasons: cos^2 theta times csc theta + sin theta.
    b. If sin^-1 (squareroot of 3 over 2) = alpha^R and alpha^R lies in quadrant II, find alpha^R, cos value and tan value.

    Can you help me with those?
    is #1. \cos^2\theta\csc\theta+\sin\theta or \cos^2\theta(\csc\theta+\sin\theta)?
    Let's say its the first...

    \cos^2\theta\csc\theta+\sin\theta=\cos^2\theta\fra  c{1}{\sin\theta}+\sin\theta=\cot\theta\cos\theta+\  sin\theta
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  7. #7
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    its cos^2 theta times(as in multiplying.. the dot) csc theta + sin theta.
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  8. #8
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jakej78 View Post
    its cos^2 theta times(as in multiplying.. the dot) csc theta + sin theta.
    so...the second one then?

    or is it

    \cos^2[\theta(\csc\theta+\sin\theta)].

    Do you know how to input commands into a graphing calculator? If so, just go ahead and type it out just like that. I'll understand what you mean.
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  9. #9
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    <br />
\cos^2\theta\bullet\csc\theta+\sin\theta<br />
    would be it..
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