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Thread: FIND A and B

  1. #1
    Member M670's Avatar
    Sep 2012

    FIND A and B

    Use an addition or subtraction formula to write the expression as a trigonometric function of one number:

    I figured out A to = 3 and B to = 1.99
    Only one of my two answer is correct I don't know which one?
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  2. #2
    MHF Contributor

    Apr 2005

    Re: FIND A and B

    The "difference formula" for cosine is cos(x- y)= cos(x)cos(y)+ sin(x)sin(y). Here, x= \frac{3\pi}{7} and y= \frac{2\pi}{21}. So x- y= =\frac{3\pi}{7}-\frac{2\pi}{21}= \frac{9\pi- 2\pi}{21}= \frac{7\pi}{21}= \frac{\pi}{3}. I don't know where you got " \frac{1.99}{2}" but \frac{\pi}{3} radians is 60 degrees. Draw an equilateral triangle with each side of length s and drop a perpendicular from one vertex to one side. That divides the triangle into two right triangles having hypotenuse of length s and one leg, the one at the 60 degree angle, of length (1/2)s. The cosine is "near side over hypotenuse", \frac{(1/2)s}{s}= \frac{1}{2}, NOT \frac{1.99}{2}.
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