I wonder why uncertainties in angle measurement MUST be in radians. For example, I want to calculate the uncertainty in measuring the function y = sin ⁡ ( θ ) when the angle is measured ± 1 degree. I do this using differential, so d y = cos ⁡ ( θ ) d θ, now d θ = ± 1 degree is the error in θ. Now, all the course notes/ books I read says this must be converted in radians, even though the angle we use here is measured in degree. How come?

Question

I wonder why uncertainties in angle measurement MUST be in radians. For example, I want to calculate the uncertainty in measuring the function   y  =  sin  ⁡  (  θ  ) when the angle is measured   ±  1 degree. I do this using differential, so   d  y  =  cos  ⁡  (  θ  )  d  θ, now   d  θ  =  ±  1 degree is the error in   θ. Now, all the course notes/ books I read says this must be converted in radians, even though the angle we use here is measured in degree. How come?

Korotnokby · Accepted Answer

Because, if you don&#039;t use radians the derivative of   sin  ⁡  θ is not   cos  ⁡  θ, and so your formula   d  y  =  cos  ⁡  θ    d  θ doesn&#039;t hold (it needs a coefficient).

Sonia Gay · Accepted Answer

They don&#039;t have to be. It is just if you don&#039;t you will have a bunch of       π    180   factors when you differentiate   sin  ⁡            π      x        180   which is the expression for sin in degrees. You could use whatever coordinate you want, but it would be silly to not use the one that makes the computation simpler.

I wonder why uncertainties in angle measurement MUST be in radians. For example, I want to calculate

Answered question

Answer & Explanation

New Questions in Pre-Algebra