You can put this solution on YOUR website! problem is:
cos(x) - sin(-x) = 0
since sin(-x) = -sin(x), equation becomes:
cos(x) + sin(x) = 0
divide both sides of this equation by cos(x) to get:
1 + tan(x) = 0
subtract 1 from both sides of this equation to get:
tan(x) = -1
use your calculator to find x = tan^-1(-1) which means find the value of x for which tan(x) = -1.
that equals -45 degrees which is equivalent to 315 degrees.
since the tan function repeats its cycle every 180 degrees, then the answer would be:
x = -45 degrees +/- 180 degrees * n, where n is the number of 180 degree cycles.
you can graph this function on algebra.com by converting the degrees to radians.
-45 degrees equals -45*pi/180 = -.7853981634 radians.
180 degrees = 180*pi/180 = pi*radians which is equal to 3.141592654 radians.
your 2 equations to graph would be:
y = cos(x)
y = sin(-x)
your graph would look like this:
the intersections of the 2 equations of cos(x) and sin(-x) on this graph would be where cos(x) = sin(-x).
that should occur at the values of x =:
-225 degrees = -3.9 radians
-45 degrees = -.8 radians
135 degrees = 2.4 radians
315 degrees = 5.5 radians
radian values are rounded to the nearest 10th because the accuracy of the graph doesn't allow better accuracy than that.
vertical lines are placed at those values of x to help you see where the intersections of the 2 equations are.
those intersections of the graph of cos(x) and sin(-x) are where cos(x) = sin(-x).
that satisfies the original equation of cos(x) - sin(-x) = 0
