Upon creating a recent exam, a colleague of mine told me that he would accept the answer $\frac{\pi}{5}$+360$^{\circ}$ as a positive coterminal angle to $\frac{\pi}{5}$. I disagreed and said that you cannot combine radians and degrees without conversion (and also that $\frac{\pi}{5}$+360$^{\circ}$ is not an angle). He says that is just semantics and that 360$^{\circ}$ is in fact, 2${\pi}$. Who is right?
When asked to find a coterminal angle, can you combine radians and degrees
trigonometry
Best Answer
While I don't think the answer is teeeeechnically wrong, it is absolutely improper to combine two uncompatible units as such. You don't tell people that they are $5$ feet and $22$ centimeters tall. I would not award credit -- and I think a reasonable expectation of students that could even arrive at an answer of $\displaystyle \frac{\pi}{5}$ for any question is that they know that $2\pi$ is the same angle as $360º$. You are in the right, and it is important to instill mathematical clarity in students.