Question

Cosx = rad(3)/2
pls help i dont understand how to solve

Answer 1

The general value of x is
`x=2n\pi\pm (\pi)/(6)`, where n is any integer. The values of x between 0 to 2π are
`(\pi)/(6)\text{ and }(11\pi)/(6)`.

Explanation:

It is given that

`\cos x=(√(3))/(2)`

We know that

`\cos (\pi)/(6)=(√(3))/(2)`

So, the given equation can be written as

`\cos x=\cos (\pi)/(6)`

`x=2n\pi\pm (\pi)/(6)`

Where, n is any integer.

For n=0,

`x=2(0)\pi\pm (\pi)/(6)=\pm (\pi)/(6)`

For n=1,

`x=2(1)\pi\pm (\pi)/(6)=2\pi\pm (\pi)/(6)=(11\pi)/(6),(13\pi)/(6)`

Therefore the general value of x is
`x=2n\pi\pm (\pi)/(6)`, where n is any integer. The values of x between 0 to 2π are
`(\pi)/(6)\text{ and }(11\pi)/(6)`.

Answer 2

Answer
x = 30° or x = (360 – 30) = 330° for value of (0≤x≥360)

Explanation
The first step is to find the anti-cosine of √3/2.
cos^(-1)⁡〖√3/2〗=30°
So, x=30°
The values of x can be many so a limit has to be given. For one complete cycle, the values of x would be.
Since cosx is positive the value of x must have been in the first quadrant and the 4th quadrant.
So, x = 30° or x = (360 – 30) = 330°