# How do you solve 3tanx+1=13?

##### 2 Answers
May 3, 2018

$x \approx 1.3258 \ldots + n \pi$, $n \in \mathbb{Z}$.

#### Explanation:

We have

$3 \tan x + 1 = 13$
$3 \tan x = 12$
$\tan x = 4$

Now, there is no 'nice' form of the answer. Instead, we can just accept that:

$x = \arctan 4$

And since the tangent function is periodic with period $\rho = n \pi$ for an integer $n$, the answer we seek is

$x = \arctan 4 + n \pi \approx 1.3258 \ldots + n \pi$, $n \in \mathbb{Z}$.

May 4, 2018

$x = {75}^{\circ} 96 + k {180}^{\circ}$

#### Explanation:

$3 \tan x + 1 = 13$

$3 \tan x = 12$

$\tan x = 4$

Calculator and unit circle give:

$x = {75.96}^{\circ} + k {180}^{\circ} , k \in \mathbb{Z}$