# How do you find the exact value in radians without using a calculator cos^-1 (1/2)?

Aug 6, 2018

${\cos}^{-} 1 \left(\frac{1}{2}\right) = {\left(\frac{\pi}{3}\right)}^{R}$

#### Explanation:

We know that ,

color(red)((1)cos^-1(costheta)=theta ,where, theta in [0,pi]

$\left(2\right) \cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$

Using $\left(2\right)$ ,we get

cos^-1(1/2)=color(red)(cos^-1(cos(pi/3)) and color(red)(pi/3 in[0,pi]

${\cos}^{-} 1 \left(\frac{1}{2}\right) = \textcolor{red}{\frac{\pi}{3}} \ldots . . \to \left[\textcolor{red}{a p p l y \left(1\right)}\right]$

Hence , ${\cos}^{-} 1 \left(\frac{1}{2}\right) = \frac{\pi}{3}$ $r a \mathrm{di} a n s$