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Mathematica Q&A: Plotting Trig Functions in Degrees
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This week’s question comes from Brian, who is a part-time math teacher:
How do you plot trigonometric functions in degrees instead of radians?
Trigonometric functions in Mathematica such as Sin[x] and Cos[x] take x to be given in radians:
To convert from degrees to radians, multiply by π ⁄ 180. This special constant is called Degree in Mathematica.
![Cos [180 Degree]](https://content.wolfram.com/sites/39/2011/03/Cos-180-Degree.gif "Cos [180 Degree]"){kind=small}
![Cos [180 Degree]](https://content.wolfram.com/sites/39/2011/03/Cos-180-Degree-output.gif "Cos [180 Degree]"){kind=small}
The symbol ° is a handy shorthand for Degree and is entered as Esc-d-e-g-Esc. You can also find this symbol in the Basic Math Assistant palette in the Palettes menu of Mathematica.
Using either Degree or °, you can plot trigonometric functions in degrees:
That answers the main question, but here’s a related hint.
When plotting trigonometric functions in degrees, you might also want to manually specify exactly where Mathematica draws tick marks. You can do this using the Ticks option:
(Here, Range[0, 360, 45] specifies the tick marks on the x axis, and Automatic uses the default tick marks on the y axis.)
The Ticks option is very flexible. You can specify where tick marks are drawn, what labels they should have, how long they are, and even colors and styles.
Download the Computable Document Format (CDF) file for this post to see how to get the custom tick marks used in this plot:
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Wouldn’t it be more logical to write it as Sin[theta] and theta is from 0° to 360°? In that case, the axis would still be labeled in radians, right? ;-) Of course, Ticks fix all that, but the notation of the code is not necessarily the most natural one.
If I understand it right, Plot[ SIn[theta], {theta,0,360} ] plots with major ticks at multiples of decades or something – still in degrees, not radians.
Good post. thanks.
This tip helped me a lot, thanks.
good article..
i’ve also try to write it in Pi based in your code…
==========================
majorticks =
Table[{\[Theta], Row[{\[Theta]}]}, {\[Theta], 0, 2 Pi,
1/3 Pi}]; minorticks =
Table[{\[Theta], Spacer[{0, 0}], {0.005, 0}}, {\[Theta], 0, 2 Pi,
1/8 Pi}];
Plot[Sin[\[Theta]], {\[Theta], 0, 2 Pi},
Ticks -> {Join[majorticks, minorticks]}]
========================
Be careful though: Working in degrees, the derivative of sine is not cosine.
This is another possibility. :-)
Plot[{Sin[theta ], Cos[theta]}, {theta, 0 Degree, 360 Degree},
Ticks -> {Range[0 Degree, 360 Degree, 45 Degree]}]
Dear Sir,
Thank you kindly for a reply.
I met an Oxford student last night and he
wrote quite a script. I found your solution
is fine.Thanks to the other bloggers too.
Brian
Merci, je n’y avait même pas pensé. exquis !