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recognize form sin(x)^2 + cos(x)^2 = 1

asked 2014-08-16 11:17:01 -0500

mgass gravatar image

Is there a way to tell sage that expressions like sin(x)^2 + cos(x)^2 are equivalent to 1? So, for instance, sage would replace/simplify an expression like sin(t+1)^2 + cos(t+1)^2 with 1.

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answered 2014-08-16 12:58:19 -0500

mgass gravatar image

Looks like trig_simplify() does the job:

f(t) = cos(t+1)^2 + sin(t+1)^2 f.trig_simplify()

t |--> 1

Where would I find this in the sage documentation if I did not know the name of the method (trig_simplify()) ?

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You're looking to use a trig identity to simplify your expression. Searching "trig identity" on the sagemath website gives [this page](http://www.sagemath.org/doc/reference/calculus/sage/symbolic/expression.html) as the first result and searching "trig simplify" gets you results, too. Likewise, googling "sagemath trig" gives 1 (!) result, the page linked above. A problem with simplifying is that there can be multiple simplified form [cos(2x), cos^2(x)-sin^2(x), 2cos^2(x)-1, 1-2sin^2(x)]. Which form result should be given as simplified?

dazedANDconfused gravatar imagedazedANDconfused ( 2014-08-16 13:40:59 -0500 )edit

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Asked: 2014-08-16 11:17:01 -0500

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Last updated: Aug 16 '14