What is Cos^(-1) [cos(-5pi/3)]?

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Answer 1 · 2015-09-21T17:44:55

$cos^-1[cos((-5pi)/3)]=pi/3$

First get the value of $cos((-5pi)/3)$

For this we need to find the acute angle associated with $(-5pi)/3$

Since $cosx$ is of period $2pi$ ,
the angle $(-5pi)/3$ is equivalent to $(2pi+(-5pi)/3)=color(red)(pi/3)$

Hence, $cos^-1[cos((-5pi)/3)]$ is the same as $color(green)(cos^-1[cos(pi/3)])$

$cos(pi/3)$ is $1/2$

So, $cos^-1[cos(pi/3)]=cos^-1(1/2)$

The function $cos^-1(a)$ is just asking us to give the angle whose cosine is $a$

Similarly, $cos^-1(1/2)=color(blue)(pi/3$

In other words, $cos^-1(1/2)$ verbally means: "the (acute) angle whose cosine is $1/2$