I had noticed that in studying trigonometric functions some fields of Math favors the radian measure such as calculus and analytic trigonometry, while others favor degree measure for instance in geometry and in solving a triagle which is I think a topic also in trigonometry.

As a question, Why is it that other fields favor radian over the other and vice versa? Thank you in advance in helping me in finding the answer to this question.

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    $\begingroup$ The more exact definitions of the trigonometric functions (like the series definition) are slightly simpler in radian form. I think degree measure is still favored in elementary geometry because it hasn't changed all that much in 2000 years and so it's just a hold-over from the ancient Greeks. It's not really a big deal which you use, though -- you can always convert between the two. $\endgroup$ – user137731 Mar 8 '15 at 14:37
  • $\begingroup$ @Bye_World, nice point, thanks. I agree that we can always convert between the two. But aside from historical value is there any other reason? $\endgroup$ – Jr Antalan Mar 8 '15 at 14:44
  • $\begingroup$ Well, the common angles -- like $30^\circ$, etc -- are integers in degree measure and irrational in radian measure, so that might scare some people (like the sailors who use degree measure usually) off radian measure. But yeah -- I think the reason we still use degrees is mostly for historical reasons. $\endgroup$ – user137731 Mar 8 '15 at 14:49
  • $\begingroup$ Really nice comment @Bye_World, thanks for your comment I realized that it might be the case. But personally I like rad more because I do not want spliting a degree into minutes and seconds. $\endgroup$ – Jr Antalan Mar 8 '15 at 14:56

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