wolframalpha fails grade 11 trig.
Posted by peeterjoot on November 9, 2009
Considering the spherical pendulum I ended up with the following quadratic form
Expanding or similar matrixes is a bit messy, and I thought I’d try to do it with software to avoid errors. Having written a symbol Geometric Algebra calculator, but not having any sort of trig reduction engine built into that. I haven’t had access to mathematica since leaving school a decade ago, so I made my calculator produce output that I could cut and paste into wolfram alpha’s online engine. Here’s the ones that I tried, for the , and terms respectively
simplify sin(phi)^4 sin(theta)^2 + cos(theta)^2 sin(phi)^2 + cos(phi)^4 sin(theta)^2 + 2cos(phi)^2 sin(phi)^2 sin(theta)^2 + cos(phi)^2 cos(theta)^2 simplify sin(phi)^2 sin(theta)^2 + cos(phi)^2 sin(theta)^2
These both reduce manually without too much effort, and one should get and respectively. Wolfram’s engine gives for the first
(Cos[ϕ]^2 + Sin[ϕ]^2) (Cos[θ]^2 + Cos[ϕ]^2 Sin[θ]^2 + Sin[θ]^2 Sin[ϕ]^2)
It misses three times! Mrs Sardi back at Central Technical School would have failed these guys.
For the less complex expression it does a bit better, but still misses the unit circle identity
Sin[θ]^2 (Cos[ϕ]^2 + Sin[ϕ]^2)
I hope that the real mathematica product does better. Perhaps it needs more time to do a better computation, and is giving up fast in its online version.
My intention was actually to see if the online engine would reduce the elements of a more slightly complex matrix than the one above. I’d done it manually and wanted to verify the output. If it can’t do these simple cases effectively, there’s probably not much point trying the more complex cases.