Question

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

Answer 1

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

Explanation:

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`