Changes between Version 3 and Version 4 of u/johannjc/scratchpad13


Ignore:
Timestamp:
03/11/16 13:54:34 (9 years ago)
Author:
Jonathan
Comment:

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  • u/johannjc/scratchpad13

    v3 v4  
    149149$\phi = \sin^{-1} \left ( -x / 2 \right )$
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     152[[Image(Screen Shot 2016-03-10 at 1.05.26 PM.png, width=400​)]]
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     154[[Image(Screen Shot 2016-03-10 at 1.37.13 PM.png,width=400)]]
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     156[[Image(Screen Shot 2016-03-10 at 1.48.34 PM.png,width=400​)]]
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    151160== Arbitrary direction ==
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    … …  
    165174$\sin{\phi} = 1 \rightarrow e = \sqrt{1 - (1 + x)^2(1-x^2-2x)} = \sqrt{1 - ( (1 + 2x + x^2)(1 - x^2 - 2x))} = \sqrt{1 - (1 - x^2 - 2x + 2x - 2x^3 - 4x^2 + x^2 - x^4 - 2x^3)} = \sqrt{1-(1  - 4x^3 - 4x^2 - x^4 )} = \sqrt{4x^2+4x^3+x^4} = 2x+x^2$
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