Question

Find all solutions in the interval [0, 2π).

cos x = sin x

Answer 1

There are a few ways to solve this problem. What level of math are you in?

Answer 2

I would recommend dividing both side by cos x

So
\[\frac{ cosx }{ \cos x } = \frac{sinx}{cosx} = 1 = \tan (x)\]

Take the arc tangent of 1, which in turns is \[\pi / 4\] (or 45 degrees)
But when taking the arc tan, there are two possible solution. If, which is when both X & Y are both negative or both positive, (first and third quadrant). We already have the first, so we need the third, which is pi/4 + pi = 5pi / 4 (225 degrees)

Answer 3

Thanks I understand now

Answer 4

Another way is to use the unit circle interpretation of sin and cos.

Then cos x = a/1. and sin x = b/1 which can only happen if a = b, which means the angle is pi/4 radians (45 degrees), or 5pi / 4.