Question

This is trigonometry I need help please

Answer 1

Given that the values of sin x and cos x are $\sin x=\frac{1}{2}$ and $\cos x=\frac{\sqrt{3}}{2}$

We need to determine the value of tan x.

The value of tan x:

Using the trigonometric identity, the formula for tan x is given by

$tan \ x=\frac{sin \ x}{cos \ x}$

Now, substituting the values  $\sin x=\frac{1}{2}$ and $\cos x=\frac{\sqrt{3}}{2}$ in the above formula, we get;

$tan \ x=\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})}$

Simplifying the terms, we have,

$tan \ x=\frac{1}{2}\times\frac{2}{\sqrt{3}}$

$tan \ x=\frac{1}{\sqrt{3}}$

Rationalizing the denominator, we get;

$tan \ x=\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}$

$tan \ x=\frac{\sqrt{3}}{3}$

Thus, the value of tan x is $tan \ x=\frac{\sqrt{3}}{3}$

Hence, Option B is the correct answer.