# How do you solve and find the value of cos(arctan(3/5))?

Dec 23, 2016

#### Answer:

$\cos \left(\arctan \left(\frac{3}{5}\right)\right) = \frac{5}{\sqrt{34}}$

#### Explanation:

Let $\arctan \left(\frac{3}{5}\right) = \theta$

Hence $\tan \theta = \frac{3}{5}$

and $\cos \left(\arctan \left(\frac{3}{5}\right)\right) = \cos \theta$

= $\frac{1}{\sec} \theta$

= $\frac{1}{\sqrt{{\sec}^{2} \theta}}$

= $\frac{1}{\sqrt{1 + {\tan}^{2} \theta}}$

= $\frac{1}{\sqrt{1 + {\left(\frac{3}{5}\right)}^{2}}}$

= $\frac{1}{\sqrt{1 + \frac{9}{25}}}$

= $\frac{1}{\sqrt{\frac{34}{25}}}$

= $\sqrt{\frac{25}{34}}$

= $\frac{5}{\sqrt{34}}$