How do you find the exact value of cos−1(cos(−π3))?

1 Answer
Bdub
Apr 15, 2016

cos−1(cos(−π3))=cos−1(cos(π3))=π3

Explanation:

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(−π3))=cos−1(cos(π3))

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

therefore,

cos−1(cos(−π3))=cos−1(cos(π3))=π3

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