Solve for 0 <x< 360 degrees
Okay this is probably a stupid question but I'm really not doing so good with this unit so far.
Apparently to get the answer you have to take a squaring approach
Square both sides
sinx=+ or - (1/sqrt(2))
45, 135, 225, 315 degrees
BUT what I would have done is
135, 315 degrees
I need someone to tell me why my thinking process would or would not work. Thanks!
EDIT: Similar question I need help with too
Here's my approach
90, 180, 270 degrees
However 270 is not an answer
I feel like I understand the concept just not getting the same answers. Any help would be GREATLY appreciated
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.