Question

What is the value of
cos−¹(cos(−π/3))?
with explanation please ​

Answer 1

$We have, \cos \theta=\cos (-\theta), \forall \theta \in \mathbb{R} \ldots \ldots \ldots \ldots$

Next let us recall the following defn. of the $\cos ^{-1}$ function :-

$\cos ^{-1} x=\theta,|x| \leq 1 \Leftrightarrow \cos \theta=x, \theta \in[0, \pi] \ldots \ldots \ldots \ldots . .(2)$

$Now, using (2) in \leftarrow direction, keeping in mind that \cos \theta \leq 1 ,$

$we have, \cos ^{-1}(\cos \theta)=\theta, \quad if , \theta \in[0, \pi] \ldots \ldots \ldots \ldots \ldots . .\left(2^{\prime}\right)$

$Now, \cos ^{-1}\left(\cos \left(-\frac{\pi}{3}\right)\right)=\cos ^{-1}\left(\cos \left(\frac{\pi}{3}\right)\right) \ldots \ldots \ldots \ldots . .[b y(1)]$

$\&, here, since \frac{\pi}{3} \in[0, \pi], we get, by \left(2^{\prime}\right)$

$\cos ^{-1}\left(\cos \left(-\frac{\pi}{3}\right)\right)=\cos ^{-1}\left(\cos \left(\frac{\pi}{3}\right)\right)=\frac{\pi}{3}$

Answer 2

Step-by-step explanation:

sᴏ ᴛʜᴇ ᴄᴏs ᴡɪʟʟ $5 ..

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