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anonymous
 one year ago
Slope of the tangent line to the polar curve r=sin(6theta). Theta =pi/12. Find slope
anonymous
 one year ago
Slope of the tangent line to the polar curve r=sin(6theta). Theta =pi/12. Find slope

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2you are looking for the slope in xy coordinates you need this: \(\huge \frac{dy}{dx} = \frac{\frac{dr}{d \theta} sin \ \theta + r \ cos \ \theta} {\frac{dr}{d \theta} cos \theta  r sin \ \theta}\) \(\large \frac{dr}{d \theta} = \frac{d}{d \theta} (sin6\theta) = 6 cos 6 \theta\) \(\large \theta = \frac{\pi}{12} \implies \frac{dr}{d \theta} = 6 cos (6 *(\frac{\pi}{12})) =6 cos (\pi/2 ) = 0\) \(\large r(\frac{\pi}{12}) = sin(6 \theta) = sin(6*\frac{\pi}{12}) = sin( \pi / 2) = 1\) \(\large \frac{dy}{dx} = cot (\frac{\pi}{12}) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what is the slope?

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.0You need the formula \[\frac{dy}{dx} = \frac{\frac{dr}{d \theta} \sin(\theta) + r*\cos(\theta)}{\frac{dr}{d \theta}\cos(\theta)  r*\sin(\theta)}\] so take the derivative of sin(6theta) and plug into the formula for example if I had 4 The derivative would be 0 so I would plug that into my formula: (0*sin(theta) + 4cos(theta) )/(0*cos(theta) 4sin(theta)) Simplify then plug Theta =pi/12 into your formula and solve and you should get your derivative

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.0in my example r = 4

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.0This video explains the method nicely https://www.youtube.com/watch?v=GkhOx4hUssA

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What would it be for me

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.23.73 i make it steep !

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.0I will give you an example one second

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.2again \( \theta\) can be blagged because \(\theta = \pi / 12\) sits on the extreme of a petal and on the circle [of radius 1]

Australopithecus
 one year ago
Best ResponseYou've already chosen the best response.0Here is the explicit answer just hit approximate for result and you will see the result I recommend you check it out

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0\(r=sin(6\theta)~ and~ \theta=\pi/12, so~ r=sin(6\pi/12)=sin(\pi/2)=1\)
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