How do you find the exact value of $cos^-1(cos((-pi)/3))$ ?

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Answer 1 · 2016-04-15T16:14:02

$cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))=pi/3$

Even Function
If f(-x) = f(x), then f is called an even function

Since cosine is an even function f(-x)=f(x) hence cos(-pi/3)=cos(pi/3)
Then
$cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))$

Now we use the property
$f^-1 f(x) = x$ , for all x in the appropriate domain

therefore,

$cos^-1(cos(-pi/3))=cos^-1(cos(pi/3))=pi/3$

How do you find the exact value of cos^-1(cos((-pi)/3))cos^-1(cos((-pi)/3))?