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Math Help - Trigonometry (circular functions)

  1. #1
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    May 2010
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    Palmy
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    Question Trigonometry (circular functions)

    Hi everyone i need help with this badly. I'm hopeless at math and can't seem to figure these questions out. It is for my pre engineering course it is pretty easy stuff but i study by correspondence and teach myself so any help would be very much appreciated!

    1A) Given cos A=0.2 and sin A=0.98
    FIND:
    a) sin(180degrees + A)
    b) cos(360degrees - A)
    c) tan(180degrees + A)
    d) cos(180degrees - A)
    e) sin(360degrees + A)

    2) Sketch the graph of y= 15 sin 2x for 0<x<360?

    3)Draw the graph of y=120cos(6theta-45degrees)?
    - what is the amplitude?
    - the period?
    - the phase shift?

    4)Given that sin 55degrees = 0.819 and cos20degrees = 0.94,
    show how you would use the identities for sin(A(plus or minus)B) and cos(A(plus or minus)B) to find the following:
    a) sin 75degrees
    b) cos 35 degrees
    c) tan 35 degrees
    Showing the steps you would follow. NOTE: sin^2theta+cos^2theta=1
    Last edited by GAVREED2; May 24th 2010 at 06:19 PM.
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  2. #2
    Junior Member
    Joined
    Oct 2009
    Posts
    54
    For question one,
    Use sin^{-1} & cos^{-1} to find the angles associated with those values you have been given. Once you've found those angles, you can evaluate the trig functions in the according to which quadrant the angle has been adjust to.

    Question 2, graph it over the domain.

    Question 3, the consider the equation  y(\theta)=Asin(c\theta + x) The amplitude is A, the period is 360/c, as sine will repeat itself after 360^{\circ}. The phase shift is x.

    Question 4, the identities you mention are as follows:
    sin(A\pm B) = sin(A)cos(B)\pm cos(A)sin(B),  cos(A\pm B)=cos(A)cos(B) \mp sin(A)sin(B). Use them to figure out how angle can be found using what you've been given.

    Hope this helps!
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