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Sin,cos problems

  1. May 12, 2004 #1
    I'm doing a review for my math class and came upon some that I cannot figure out.I don't know why I cannot get the right answer. I know all the rules, I've had tests on this stuff and received A's but these are different for some reason and I don't know why. If anyone can do even one of them I would so greatly appreciate it! my exam is tomarrow :cry: thanks




    let sin(x)=5/13, cos(x)=12/13, sin(y)=4/5 and y is in Quadrant II and 0<or=to x <2pi

    81. sin(x-y)=____

    83. sin 2x =___

    84. sin x/2 =___

    now the rules above don't apply to these below

    85. sin(pheta)=2/3 and 0<pheta<90 then cos2(pheta)=___

    86.sin(2cos^-1(1/4))=___
     
  2. jcsd
  3. May 13, 2004 #2

    arildno

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    1.
    Determine the cosine value of y:
    You are given that y is in Quadrant 2, which means that the cosine value of y is negative (Agreed?)

    In order to determine the cosine value of y, use the fundamental identity:
    [tex] \cos^{2}y+\sin^{2}y=1.[/tex]
    Knowing that the cosine value has to be negative, you should be able to figure out the answer.
    2. 81,82,83:
    Knowing the summation, double angle, half-angle formulae for the trigonometric functions should now give you the answers.
    3.
    85:
    [tex] \sin^{2}\theta=\frac{1-\cos(2\theta)}{2}[/tex]
    4.86:
    [tex]
    \sin(2\phi)=2\sin\phi\cos\phi, \sin\phi=\pm\sqrt{1-\cos^{2}\phi}[/tex]
     
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