Math CentralQuandaries & Queries


Question from a student:


to evaluate f(30)

use radians only or degrees



In this question you are asked to add $x$ and $\sin(x).$ Regardless of the units that you use for $x$ the quantity $\sin(x)$ is a pure number, it has no units. You can't add this quantity to $x$ unless $x$ is also a pure number. That's the old expression "You can't add apples and oranges." Hence if $x$ is in the units degrees you can't add it to $\sin(x).$

A radian is a pure number, it has no units and hence if $x$ is measured in radians you can add $x$ and $\sin(x).$

To evaluate $x + \sin(x)$ when $x = 30$ set your calculator to radians and calculate $\sin(30).$ if you get the answer 0.50 then your calculator is set to degrees so try again.


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