the quadratic equation allowed you to discover the 2 possible values for
Now you need to find the valid values of the angle x.
may be conveniently thought of as the vertical co-ordinate
of a point on a circle centred at (0,0) with radius 1.
Then you can see, using a sketch that a vertical co-ordinate of
gives 2 possible angles,
For on the vertical axis,
you can calculate the acute angle
to get the acute angle the point on the circle makes under the x-axis.
Then subtract this from 360 degrees and add it to 180 degrees.
You really need to understand that procedure
it may not always be brought across as
in a circle, centre (0,0) and radius 1
However, i feel it's quite easy to work with that way.
You may instead be presented with
sin is + in the 1st and 2nd quadrants, sin is - in the 3rd and 4th.
cos is + in the 1st and 4th quadrants, cos is - in the 2nd and 3rd.
Hence for your positive answer for sinx,
this corresponds to one angle in the 1st quadrant, 0 to 90 degrees
and another angle in the 2nd quadrant, 90 to 180 degrees.
Then work from there knowing that the angle in the 2nd quadrant is 180-(angle in 1st)
Similarly for cos, using the guidelines for that.
i much prefer the horizontal and vertical co-ordinates way,
after all that's why we can give sin and cos their polarities in the 4 quadrants.
Whichever way you do it, remember sinx points out 2 angles as does cosx.