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anonymous
 one year ago
Velocity/tangent vector example #2 (see link below): how do we know what trigonometric identities to apply? The example seemingly arbitrarily chooses to reexpress everything in terms of the halfangle. On a normal problem, is there any indication as to what identities should be used? Or alternatively, is there a solution with only simple identities (I tried but couldn't simplify it enough)?
http://ocw.mit.edu/courses/mathematics/1802scmultivariablecalculusfall2010/1.vectorsandmatrices/partcparametricequationsforcurves/session20velocityandarclength/MIT18_02SC_we_11_comb.pdf
anonymous
 one year ago
Velocity/tangent vector example #2 (see link below): how do we know what trigonometric identities to apply? The example seemingly arbitrarily chooses to reexpress everything in terms of the halfangle. On a normal problem, is there any indication as to what identities should be used? Or alternatively, is there a solution with only simple identities (I tried but couldn't simplify it enough)? http://ocw.mit.edu/courses/mathematics/1802scmultivariablecalculusfall2010/1.vectorsandmatrices/partcparametricequationsforcurves/session20velocityandarclength/MIT18_02SC_we_11_comb.pdf

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phi
 one year ago
Best ResponseYou've already chosen the best response.1You could leave the answer in terms of theta rather than theta/2 However, when you integrate to find the arc length I believe you will want to do a trig substitution. At that point you might go back and simplify your previous expressions using that same substitution...
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