Question

Explain why it is sometimes necessary to express the values of angle theta in radians rather than degrees.

Answer 1

well for one thing, trigonometric functions are functions whose domain in numbers, not angles.
as such, these functions correspond to the functions of angles only if the angles are measured in radians, not in degrees

Answer 2

just like if i say let
\[f(x)=x^2\] you would just assume that x could be any number, and not ask me if x was measured in degrees or radians, or for that matter celsius or fahrenheit, or feet or meters.

Answer 3

if you have had calc you may know that the derivative of sine is cosine. but that is in fact false(!) if we are considering the input to be angles measured in radians