I have read in some math manuals that a quick way to check whether your calculator is in radian mode or degree mode is to take the Cosine of 90. If your calculator is in degree mode the answer is 0, and not 0 (~ -0.448) if your calculator is in radian mode. Now if we knew nothing about trigonometry we might prefer to take the Cosine of 0. But we do know something about trigonometry. The Cosine of 0 is 1 (cos(0) = 1) in both degree and radian mode, so 0 cannot be used to check the mode of your calculator.
My question to you is:

Find all numbers so that the Cosine of that number is the same in degree mode as it is in radian mode.
In fact, we might as well also do this for the Sine and Tangent functions.

Exact answers only, but here is a decimal approximation of one value that works for sine: x ~ 3.08770208587.
sin(3.08770208587) ~ 0.05386448674 in both radian and degree mode.