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Math Help - Trigonometry Questions and identities.

  1. #1
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    Trigonometry Questions and identities.

    Could someone please solve these questions. I am struggling with them. Very much appreciated. Donation will be provided

    (i) If Cosec theta = 3.2 find theta (in degrees) 0<theta<360

    (ii) If sin theta= .7 write down values for
    a - sin (180 - theta)
    b - sin (360 - theta)

    (iii) Using the identity sin^2theta + cos^2theta=1 and the identities for cos(A+B) find:
    a - cos 75degrees if cos 45degrees = .707
    b - cos 30degrees = 0.866

    (iv) Prove that sinx/1-cosx + sinx/1+cosx= 2 cosecx
    Last edited by mr fantastic; October 23rd 2010 at 10:12 PM. Reason: Edited title.
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  2. #2
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    (i) \csc (\theta) = 3.2

    \frac{1}{\sin (\theta)}= 3.2

    1= 3.2 \cdot \sin (\theta)

    \frac{1}{3.2}=\sin (\theta)

    \sin^{-1} \bigg( \frac{1}{3.2} \bigg)=\theta


    (ii) \sin \theta = 0.7

    \theta = \sin^{-1} (0.7)

    Solve for theta and then you can put it into your other 2 equations. What are the values of a and b?
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  3. #3
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    (iv) \frac{\sin x}{1-\cos x} + \frac{\sin x}{1 + \cos x}

    Cross multiply to get the same denominator:

    =\dfrac{(\sin x)(1+ \cos x)}{(1+ \cos x)(1-\cos x)} + \dfrac{(\sin x)(1-\cos x)}{(1 + \cos x)(1 - \cos x)}

    =\dfrac{(\sin x)(1+ \cos x)+(\sin x)(1-\cos x)}{(1+ \cos x)(1-\cos x)}

    Expand brackets and group like terms:

    =\dfrac{2 \sin (x)}{1 - \cos^2 (x)}

    Now use the pythagorean identity \sin^2 x + cos^2 x = 1 to get your answer.
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  4. #4
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    Thankyou so much for your help. I was able to understand what i actually had to do much better. I am fairly new to trigonometry.

    For the proof would this be correct. following on from the last line you gave me.

    2sin(x)/1-cos^2(x)
    {sin(x)/1-cos(x)} + {sin(x)/1+cos(x)} = 2sec(x)
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  5. #5
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    That doesn't prove the trigonometric identity yet, and it is also incorrect (it should be 2csc(x)).

    Remember that 2 \csc x = \frac{2}{\sin x}

    What I had in mind was substituting 1 - \cos^2 x with \sin^2 x and the simplifying to get your answer.
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  6. #6
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    ok sorry i'm not very confident with trig. So:

    2sin(x)/1-cos^2(x)=2csc(x)
    2sin(x)/sin^2(x) =2csc(x)
    2/sin(x) =2csc(x)

    Is this now a proven identity
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  7. #7
    MHF Contributor harish21's Avatar
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    Yes!

    Because csc(x)=1/sin(x)
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