cheesynooby
Well-Known Member
oh whoops sorry i thought u meant why they did all those different solutions, not how they got thereI apologise. I meant the highlighted section.
sinx is periodic (with a period of 2π) so if ur working out the solutions to sinx = something there will be infinite solutions.
adding/subtracting an integer multiple of 2π to any solutions u get for the range from 0 to 2π will thus also work (since the sine curve repeats every 2π)
from considering the unit circle, u can get that there is a solution in the 3rd quadrant and 4th quadrant which gives u the solutions for 0 ≤ 2theta ≤ 2π
(u could think of this as the angle such that the point on the unit circle as a y coordinate of -sqrt3/2 which is in the 3rd and 4th quadrant)
to get for -2π ≤ 2theta ≤ 2π therefore u subtract 2π from each of those 2 solutions.
