Question

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

Answer 1

`color(blue)(x = 26.565051)`

Explanation:

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

`tan` `theta` `=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)

`(canceltan theta/canceltan ) = ((1/2)/tan)`
`theta = (1/2)*(1/tan)`
`theta = arctan(1/2)`

arctan `(1/tan) or tan^-1` is the inverse function of tan function,

`theta = tan^-1(1/2)`

`theta = 26.565051`

Answer 2

`t = 26^@57 + k360^@`

Explanation:

`tan t = 1/2`
Calculator and unit circle give 2 solutions for (0, 360) -->
`t = 26^@57` , and `t = 180 + 26.57 = 206^@57`
General answer:
`t = 26^@57 + k360^@`