Question

find all solutions in interval [0, 2pi) in: sinx - cos x = 0

Answer 1

At what points on the edge of a circle are the x coordinate and y coordinate equal?

Answer 2

at pi/4 and 5pi/4 so thats the answer?

Answer 3

yep

Answer 4

for showing work .. what do I have to do though ?

Answer 5

Well, you could always draw the unit circle and the line y = x, and say the intersection points are those places where sin(x) = cos(x)

Answer 6

what about that ( -) sign what does it mean thats what throws me off

Answer 7

Or you could get fancy and multiply both sides by sin(x) + cos(x), in which case you'd find
\[ \sin^2(x) - \cos^2(x) = 0 \rightarrow \sin^2(x) - \left[ 1 - \sin^2(x) \right] = 2\sin^2(x) - 1 = 0\]
so
\[\sin^2(x) = 1/2\]
and the rest follows from there. What minus sign are you talking about?

Answer 8

sin(x) - cos(x) = 0 and sin(x) = cos(x) mean exactly the same thing.

Answer 9

yea I just realized wow. haha thank you so much. all the problems were harder and that one so simple just confused me