Author Topic: Parametric equations in further trig (Read 1121 times) Tweet Share

hinakamishiro · « **on:** July 24, 2016, 11:44:17 am »

Hey guys!
I was wondering if anyone could explain parametric equations in the context of trig? Using compound, double abd triple angle theorums etc. I've attached questions for reference. Thank you!

RuiAce · « **Reply #1 on:** July 24, 2016, 11:54:47 am »

Quote from: hinakamishiro on July 24, 2016, 11:44:17 am

Hey guys!
I was wondering if anyone could explain parametric equations in the context of trig? Using compound, double abd triple angle theorums etc. I've attached questions for reference. Thank you!

$\text{Have an objective. No matter what you do, you always want to eliminate the parameter. In these cases, }\theta\\ \text{Take d), cause it looks weirder (upon a bit of seeing ahead)}$
$\text{We can immediately expand out }y=12\sin \theta\cos\theta\\ \text{And immediately substitute in }x=3\sin \theta\\ \text{But there is still a }\cos\theta\text{ we need to cater for some how (Pythagorean identity).}\\ \textit{Use of a Pythagorean identity isn't shocking generally speaking for trigonometric parametrisations.}$
$y=4x\cos\theta\implies y^2=16x^2\cos^2\theta\\ \therefore y^2=16x^2(1-\sin^2\theta)\\ \text{which you can substitute }\sin\theta=\frac{x}{3}\text{ to obtain an answer.}$

hinakamishiro · « **Reply #2 on:** July 24, 2016, 12:16:46 pm »

Quote from: RuiAce on July 24, 2016, 11:54:47 am

$\text{Have an objective. No matter what you do, you always want to eliminate the parameter. In these cases, }\theta\\ \text{Take d), cause it looks weirder (upon a bit of seeing ahead)}$
$\text{We can immediately expand out }y=12\sin \theta\cos\theta\\ \text{And immediately substitute in }x=3\sin \theta\\ \text{But there is still a }\cos\theta\text{ we need to cater for some how (Pythagorean identity).}\\ \textit{Use of a Pythagorean identity isn't shocking generally speaking for trigonometric parametrisations.}$
$y=4x\cos\theta\implies y^2=16x^2\cos^2\theta\\ \therefore y^2=16x^2(1-\sin^2\theta)\\ \text{which you can substitute }\sin\theta=\frac{x}{3}\text{ to obtain an answer.}$

Thank you! This really helped! You're brilliant thanks

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Author Topic: Parametric equations in further trig (Read 1121 times) Tweet Share

hinakamishiro

Parametric equations in further trig

RuiAce

Re: Parametric equations in further trig

hinakamishiro

Re: Parametric equations in further trig

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