Need a half-angle identity if anybody knows one...

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Need a half-angle identity if anybody knows one...

Postby Yablon » Sun Sep 01, 2019 12:05 pm

Hi all:

You will all know the trigonometric half-angle identity for .

Can someone please figure out, or does someone know, something similar for the following?





Either point to a trigonometry reference, or please show us how you get there. I am concerned about the body of the functions, more so than the signs.

Thanks,

Jay
Yablon
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Re: Need a half-angle identity if anybody knows one...

Postby Yablon » Sun Sep 01, 2019 1:10 pm

Yablon wrote:Hi all:

You will all know the trigonometric half-angle identity for .

Can someone please figure out, or does someone know, something similar for the following?





Either point to a trigonometry reference, or please show us how you get there. I am concerned about the body of the functions, more so than the signs.

Thanks,

Jay

OK, what I derived from half angle formulas for sin, cos and tan, via cos^2 and sin^2, is the following:





I would have to say that the original expressions in this case are simpler than those with half angles. Anybody see anything else?

Jay
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Location: New York

Re: Need a half-angle identity if anybody knows one...

Postby FrediFizzx » Sun Sep 01, 2019 1:22 pm

Yablon wrote:
Yablon wrote:Hi all:

You will all know the trigonometric half-angle identity for .

Can someone please figure out, or does someone know, something similar for the following?





Either point to a trigonometry reference, or please show us how you get there. I am concerned about the body of the functions, more so than the signs.

Thanks,

Jay

OK, what I derived from half angle formulas for sin, cos and tan, via cos^2 and sin^2, is the following:





I would have to say that the original expressions in this case are simpler than those with half angles. Anybody see anything else?

Jay

Mathematica gives for the first one,



And the second one,


.
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Re: Need a half-angle identity if anybody knows one...

Postby FrediFizzx » Sun Sep 01, 2019 7:54 pm

FrediFizzx wrote:
Yablon wrote:OK, what I derived from half angle formulas for sin, cos and tan, via cos^2 and sin^2, is the following:





I would have to say that the original expressions in this case are simpler than those with half angles. Anybody see anything else?

Jay

Mathematica gives for the first one,



And the second one,


.

Here is a spherical plot of the first one. The side you can't see is just a round sphere.

Image
.
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Independent Physics Researcher
 
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Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA


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