Question

Question #f0b60

Answer 1

`A = 150^@+2*360^@`
and `210^@+n*360^@`
`color(white)("XXXXXXXXXXXXXXXXXX")"for "AAn in ZZ`

Explanation:

`2cos(A)+sqrt(3)`

`rarrcolor(white)("XXX")2cos(A)= -sqrt(3)`

`rarrcolor(white)("XXX")cos(A)= -sqrt(3)/2`

The image below shows the possible angles for this:

The angle in Quadrant II is `180^@-30^@ = 150^@`

The angle in Quadrant III is `180^@ + 30^@ = 210^@`

Obviously any additional full rotations (multiples of `360^@`) would also need to be included in order to specify all possible solutions.

If you prefer your answer in radians
`A = (5pi)/6+n*2pi`
and `(7pi)/6+n*2pi`
`color(white)("XXXXXXXXX")AAn in ZZ`