Question 504787: The function arccos is defined as the inverse of the cosine function restricted to the interval [0,π]. Suppose we define a function f by f(x)=cos(x) for x in the interval [-π,0] and let g be the inverse function to f. find g(-1/2) and g(2^(1/2))/2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The function arccos is defined as the inverse of the cosine function restricted to the interval [0,π].
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Suppose we define a function f by f(x)=cos(x) for x in the interval [-π,0] and let g be the inverse function to f.
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find g(-1/2)
g(-1/2) = f^-1(-1/2) = arccos(-1/2) = 240 degrees or (-2/3)pi
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g(2^(1/2))/2 = g(1/8)/2 = f^-1(1/8)/2 = (1/2)arccos(-1/8) = (1/2)(-97.18)
= -48.59 degrees = -48.59(pi/180) = -0.2699(pi)
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Cheers,
Stan H.
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