Verified Answer :

IsrarAwan

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:

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 \(\tan x=\sqrt{3}\)

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