Exact values of a Trigonometric function

anna_sims

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Oct 26, 2006
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I need to find 3 exact values of the function y=3+5cos(1/4)(x-240degrees) within the interval of 240-600 degrees, not including x values of 240 or 600.

I found one point (480, 5+(1/2)), but I need help in finding the other two.
 
This one is fun:

(43π+4asin(35),0)\displaystyle (\frac{4}{3}*\pi+4*asin(\frac{3}{5}),0)

With what values of cosine are you familiar? Find values for 'x' that produce those known reference angles.

240º = 43π\displaystyle \frac{4}{3}\pi

600º = 103π\displaystyle \frac{10}{3}\pi

2π14=8π\displaystyle \frac{2\pi}{\frac{1}{4}} = 8\pi <== The Period of your function.

32π\displaystyle \frac{3}{2}\pi, for example. cos(32π\displaystyle \frac{3}{2}\pi) = 0

14(x43π)=32π\displaystyle \frac{1}{4}*(x-\frac{4}{3}\pi) = \frac{3}{2}\pi

x43π=6π\displaystyle x-\frac{4}{3}\pi = 6\pi

x=223π\displaystyle x = \frac{22}{3}\pi

By Symmetry, this works out to 103π\displaystyle \frac{10}{3}\pi which you state we don't get to use.

Pick another one.

cos(π6)=32\displaystyle cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}

π6=14(x43π)\displaystyle \frac{\pi}{6} = \frac{1}{4}*(x-\frac{4}{3}\pi)

This leads to x = 2π\displaystyle 2\pi which is in your Domain. (2π,3523)\displaystyle (2\pi,3-\frac{5}{2}\sqrt{3})
 
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