On an interval of [0, 2π), can the sine and cosine values of a radian measure ever be equal? If so, enter the radian measure (s) where the values are equal. If not, enter DNE. (Enter your answers as a comma-separated list.)

Yes, they are equal in the values (in radians):

π/4, 5π/4

If cos (x) and sin (x) are defined to you as nonnegative functions (in terms of lengths), then 3π/4 and 7π/4 are also included

Step-by-step explanation:

Remember that odd multiples of 45° are special angles, with the same sine and cosine values (you can prove this, for example, by considering a right triangle with an angle of 45° and hypotenuse with length 1, and finding the trigonometric ratios).

The radian measure of 45° corresponds to π/4, hence the odd multiples on the interval [0, 2π) are π/4, 3π/4, 5π/4, 7π/4.

If you define sin (x) and cos (x) using the cartesian coordinate system (via unit circle), then cos (3π/4) = -sin (3π/4) and cos (7π/4) = -sin (7π/4). In this case, only π/4 and 5π/4 are valid choices.