Question

If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Answer 1

The correct answers are:
1) sin(x) = $\frac{ \sqrt{3} }{2}$
2) tan(x) = $\sqrt{3}$

Explanation:
Given:
$cos(x) = \frac{1}{2}$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( \frac{1}{2} )^2 = 1 \\ sin^2(x) + \frac{1}{4} = 1 \\ sin^2(x) = \frac{3}{4}$

Step 3:
Take square-root on both sides:
$\sqrt{sin^2(x)} = \sqrt{\frac{3}{4}}$

sin(x) = $\frac{ \sqrt{3} }{2}$

Now to find the tan(x), we would use the following formula:

tan(x) = $\frac{sin(x)}{cos(x)}$ --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $\frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} }$

Hence tan(x) = $\sqrt{3}$

Answer 2

Answer:

The value of $\sin x=\frac{\sqrt{3}}{2}$

The value of $\tan x=\sqrt{3}$

Step-by-step explanation:

Given = $\cos x=\frac{1}{2}$

To find :$\sin x=?$ and $\tan x=?$

Solution:

We know that, if the cosine function of an angle is$\frac{1}{2}$ then the angle is equal to the 60°.

$\cos x=\frac{1}{2}$

x = 60°

The value of the :

$\sin x=\sin 60^o=\frac{\sqrt{3}}{2}$

We know that ratio of sine function to the cosine function is equal tto the tangent

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

The value of $\sin x=\frac{\sqrt{3}}{2}$

The value of $\tan x=\sqrt{3}$