Question

Find all solutions in the interval [0, 2π). cos x = sin x

Answer 1

The interval covers the entire circle. Think of a unit circle with points (cos x, sin x). At which angles do these two values equal?

Hint: sin x is positive in the I and II quadrant, and negative elsewhere.
cos x is positive in the I and IV quadrant, and negative elsewhere.

So if sin x = cos x, this would have to take place in quadrant I (where they are both positive) or quadrant III (where they are both negative)

Answer 2

Thank you so much!

Answer 3

if you divide both sides by cos x, you have an equation in one trigonometric functions instead of two.

Answer 4

The lengths of the lines correspond with the values of cos x and sin x. If they are equal sides, can you determine what angle corresponds with them?