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)
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.
Asked: 2011-11-16 20:54:41 +0200
Seen: 4,492 times
Last updated: Nov 16 '11
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