Respuesta :

IsrarAwan
The correct answers are:
1) sin(x) = [tex]\frac{ \sqrt{3} }{2} [/tex]
2) tan(x) = [tex] \sqrt{3} [/tex]

Explanation:
Given:
[tex]cos(x) = \frac{1}{2} [/tex]

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

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

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

sin(x) = [tex]\frac{ \sqrt{3} }{2} [/tex]

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

tan(x) = [tex] \frac{sin(x)}{cos(x)} [/tex] --- (2)

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

Hence tan(x) = [tex] \sqrt{3} [/tex]

Answer:

The value of [tex]\sin x=\frac{\sqrt{3}}{2}[/tex]

The value of [tex]\tan x=\sqrt{3}[/tex]

Step-by-step explanation:

Given = [tex]\cos x=\frac{1}{2}[/tex]

To find :[tex]\sin x=?[/tex] and [tex]\tan x=?[/tex]

Solution:

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

[tex]\cos x=\frac{1}{2}[/tex]

x = 60°

The value of the :

[tex]\sin x=\sin 60^o=\frac{\sqrt{3}}{2}[/tex]

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

[tex]\tan x=\frac{\sin x}{\cos x}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}[/tex]

The value of [tex]\sin x=\frac{\sqrt{3}}{2}[/tex]

The value of [tex]\tan x=\sqrt{3}[/tex]

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