# How do you evaluate Tan^-1(2.8/4)?

Aug 15, 2016

arctan 0.7 = 35.0°

#### Explanation:

The question is asking for the size of the angle which will have the length of the opposite side as 2.8 and the adjacent side 4.
${\tan}^{- 1}$ is called arctan and must not be confused with $\frac{1}{\tan \theta}$ which is called $\cot \theta$

This can only be done by using a calculator or from tables.
On a calculator use the shift/alt/2nd function key and the ${\tan}^{- 1}$ key

$2.8 \div 4 = 0.7$

arctan 0.7 = 35.0°

This is another way of saying that in a right-angled triangle with an angle of 35.0°, the opposite side will be 70% of the length of the adjacent side.