# How do you solve tan(x)=1/2?

Feb 21, 2016

$\textcolor{b l u e}{x = 26.565051}$

#### Explanation:

Since the given is a "Trigonometric Function of Tangent (Tan)",
and $x$ is an angle $\theta$ (Theta),

$\tan$ $\theta$$= \frac{1}{2}$

to get the value of $x$ or $\theta$, we can use some algebraic techniques to isolate the variable $\theta$ from $\tan$,

By simply transposing $\tan$ on both sides (Golden Rule of Algebra) - (Balancing All Sides of the Equation)

$\left(\cancel{\tan} \frac{\theta}{\cancel{\tan}}\right) = \left(\frac{\frac{1}{2}}{\tan}\right)$
$\theta = \left(\frac{1}{2}\right) \cdot \left(\frac{1}{\tan}\right)$
$\theta = \arctan \left(\frac{1}{2}\right)$

arctan $\left(\frac{1}{\tan}\right) \mathmr{and} {\tan}^{-} 1$ is the inverse function of tan function,

$\theta = {\tan}^{-} 1 \left(\frac{1}{2}\right)$

$\theta = 26.565051$

Dec 18, 2017

$t = {26}^{\circ} 57 + k {360}^{\circ}$

#### Explanation:

$\tan t = \frac{1}{2}$
Calculator and unit circle give 2 solutions for (0, 360) -->
$t = {26}^{\circ} 57$ , and $t = 180 + 26.57 = {206}^{\circ} 57$
$t = {26}^{\circ} 57 + k {360}^{\circ}$