Question

In the interval 0 degrees < x < 360 degrees, find the values of x for which tan x = 2.7475. Give your answers to the nearest degree.

Answer 1

Answer:

Thus, the values of x are 70° and 250°

Step-by-step explanation:

Trigonometric Functions

The tangent is defined as:

$\displaystyle \tan\theta=\frac{\sin\theta}{\cos\theta}$

Given a value for the tangent, there are two angles with the same tangent, one of them being $\theta$ and the other $\theta$+180°.

We are given:

$\tan x=2.7475$

The angle is the inverse tangent:

$x=arctan (2.7475)$

Using a scientific calculator, we find the first angle:

x=70°

The second angle is found adding 180°:

x=70°+180°=250°

Thus, the values of x are 70° and 250°