Question

Solve cos(x)=0.13 where 0≤x<2π There are two solutions, A and B, with A < B ?

can someone help me with this?

Answer 1

`color(blue)(arccos(13/100) and pi-arccos(13/100))`

Explanation:

`0.13=13/100`

`cosx=13/100`

`x=arccos(cosx)=arccos(13/100)=>`

`x=arccos(13/100)+n2pi`

`x=2pi-arccos(13/100)+n2pi`

`n in ZZ`

These are the general solutions. For:

`[0,2pi)`

With `n=0`

`color(blue)(arccos(13/100) and pi-arccos(13/100))`

If `A=arccos(13/100)`

Then:

`A < B`

`arccos(13/100)< pi-arccos(13/100)`

Approximate values:

`A=arccos(13/100)~~1.440427347`

`B=pi-arccos(13/100)~~1.701165307`

`1.440427347 < 1.701165307`