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Arctan(tan(2pi/3))

asked 2011-11-16 13:54:41 -0600

Bakes gravatar image

updated 2015-05-24 14:05:49 -0600

FrédéricC gravatar image

i know it looks like the short cut is applicable here. But isn't there a second point on the unit circle with the same tangent as 2pi/3? Tan(2pi/3)= -(Sqr.rt. 3) There are other places with the same value for tangent. 5pi/3 Tan(5pi/3)= -(Sqr.rt. 3)

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answered 2011-11-16 15:08:44 -0600

kcrisman gravatar image

I'm not sure what you're asking. Let us know if this is not it.

sage: arctan(tan(2*pi/3))
arctan(-sqrt(3))

Notice Sage doesn't automatically simplify this, although

sage: arctan(0)
0
sage: arctan(1)
1/4*pi

You have to do this.

sage: arctan(tan(2*pi/3)).simplify()
-1/3*pi

To get other branches, you'll want to think about arctan2.

sage: arctan2(tan(2*pi/3),1).simplify()
-1/3*pi
sage: arctan2(-tan(2*pi/3),-1).simplify()
2/3*pi

You can do

sage: arctan2?

for more details.

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Asked: 2011-11-16 13:54:41 -0600

Seen: 3,300 times

Last updated: Nov 16 '11