document.write( "Question 1197163: If −𝜋 ≤ 𝑥 ≤ 0, then cos−1(cos 𝑥) is:
\n" ); document.write( "A)𝑥 B)𝜋−𝑥 C)2𝜋+𝑥 D)2𝜋−𝑥 E)None \n" ); document.write( "

Algebra.Com's Answer #830306 by greenestamps(13241) $\"\"$ $\"About$

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\n" ); document.write( "For the inverse cosine function, the input is a real number between -1 and +1, and the output value is in a range which is the interval closest to 0 in which cos(x) takes on all it values.

\n" ); document.write( "cos(x) takes on all its values on [0,pi), so the output of the inverse cosine function is on that interval. Note cos(x) also takes on all its value on [-pi,0); but the convention is to use the interval where the numbers are positive.

\n" ); document.write( "cos(x) has a period of 2pi, so cos^(-1)(cos(x)) returns a value equal to x, plus or minus the multiple of 2pi that makes the output value between 0 and pi.

\n" ); document.write( "Since in this problem the input value x is between -pi and 0, the output value needs to be x+2pi.

\n" ); document.write( "ANSWER: C

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