Question

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

Answer 1

The value of
`\sin x=(√(3))/(2)`

The value of
`\tan x=√(3)`

Step-by-step explanation:

Given =
`\cos x=(1)/(2)`

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

Solution:

We know that, if the cosine function of an angle is
`(1)/(2)` then the angle is equal to the 60°.

`\cos x=(1)/(2)`

x = 60°

The value of the :

`\sin x=\sin 60^o=(√(3))/(2)`

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

`\tan x=(\sin x)/(\cos x)=((√(3))/(2))/((1)/(2))=√(3)`

The value of
`\sin x=(√(3))/(2)`

The value of
`\tan x=√(3)`

Answer 2

The correct answers are:
1) sin(x) =
`( √(3) )/(2)`
2) tan(x) =
`√(3)`

Step-by-step explanation:
Given:

`cos(x) = (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) + ( (1)/(2) )^2 = 1 \\ sin^2(x) + (1)/(4) = 1 \\ sin^2(x) = (3)/(4)`

Step 3:
Take square-root on both sides:

`√(sin^2(x)) = \sqrt{(3)/(4)}`

sin(x) =
`( √(3) )/(2)`

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

tan(x) =
`(sin(x))/(cos(x))` --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) =
`( ( √(3) )/(2) )/( (1)/(2) )`

Hence tan(x) =
`√(3)`