Why do we have to use radians instead of degrees?

Radians are used a lot in A level maths because at higher levels, they allow for simplification of trigonometric functions. For example, when using radians, it can be said that:

Sin(angle) ≈ angle Cos(angle) ≈ 1 - 0.5*angle ≈ 1 Tan(angle) ≈ angle

In degrees for example, it can not be said that sin(30) ≈ 30, because sin(30)=0.5 and so the approximation is way off. But radians are defined in a way that means the above equations can be assumed true, and hence complex mathematical equations can be simplified allowing them to be solved.