solving an equation by squaring both sides sometimes introduces extraneous (invalid) solutions ... that's why you need to check all solutions when you use this technique. the steps you took were fine ... just remember to check the solutions.
I feel like I understand the concept just not getting the same answers. Any help would be GREATLY appreciated
Jul 24th 2011, 12:55 AM
In general you can say for trigoniometric equations:
Jul 24th 2011, 02:16 AM
As skeeter stated, after squaring both sides you must check the solutions.
For example, in the first quadrant, both Sinx and Cosx are non-negative
and hence they cannot sum to zero.
Cosx is zero at multiples of 90 degrees and Sinx is zero at 0 degrees and multiples of 180 degrees,
so they are never zero for the same x.
Solutions to Cosx+Sinx=0 require they be opposite signs,
which occurs in quadrants 2 and 4.
Also, their numerical magnitudes (moduli) must be equal in order to cancel and get zero,
and hence they lie at the point of intersection of the line of slope -1 going through the origin
and the circumference of the unit circle.
Jul 24th 2011, 07:21 AM
All of that explained it so much better than my book. Thanks for all the help!