• anonymous
Velocity/tangent vector example #2 (see link below): how do we know what trigonometric identities to apply? The example seemingly arbitrarily chooses to re-express everything in terms of the half-angle. 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)?
OCW Scholar - Multivariable Calculus
  • Stacey Warren - Expert
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  • katieb
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  • phi
You 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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