Problems for calculus withparametric curves.

**dylan5188** · March 23rd 2010, 03:47 PM

1.Find the length of the polar curve given by

on the interval

.

I know how to do it with x and y, but what to do with this one?

Also same problem with this question

2.For what values of

on the polar curve

, with

, are the tangent lines horizontal? Vertical?

Isn't just tangent=0 and tangent=1?

**skeeter** · March 23rd 2010, 04:15 PM

Originally Posted by dylan5188

1.Find the length of the polar curve given by

on the interval

.

I know how to do it with x and y, but what to do with this one?

Also same problem with this question

2.For what values of

on the polar curve

, with

, are the tangent lines horizontal? Vertical?

Isn't just tangent=0 and tangent=1?

1. $S = \int_{\theta_1}^{\theta_2} \sqrt{r^2 + \left(\frac{dr}{d\theta}\right)^2} \, d\theta$

2. vertical tangent lines occur where $\frac{dy}{dx}$ is undefined

horizontal tangent lines occur where $\frac{dy}{dx}$ equals zero

$\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

where $y = r\sin{\theta} = \theta\sin{\theta}$

and $x = r\cos{\theta} = \theta\cos{\theta}$

**pickslides** · March 23rd 2010, 04:20 PM

Originally Posted by dylan5188

1.Find the length of the polar curve given by

on the interval

.

try $L = \int_0^{\frac{1}{6}}\sqrt{1+(3.6e^{0.4\theta})^2}~ d\theta$

**dylan5188** · March 23rd 2010, 04:46 PM

2. vertical tangent lines occur where $\frac{dy}{dx}$ is undefined

horizontal tangent lines occur where $\frac{dy}{dx}$ equals zero

$\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

where $y = r\sin{\theta} = \theta\sin{\theta}$

and $x = r\cos{\theta} = \theta\cos{\theta}$ [/quote]

So I got theta=tantheta when horizontal tangent occur
and theta=cotangent theta when vertical tangent occur. Then How to calculate them?

**skeeter** · March 23rd 2010, 05:00 PM

Originally Posted by dylan5188

2. vertical tangent lines occur where $\frac{dy}{dx}$ is undefined

horizontal tangent lines occur where $\frac{dy}{dx}$ equals zero

$\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

where $y = r\sin{\theta} = \theta\sin{\theta}$

and $x = r\cos{\theta} = \theta\cos{\theta}$

So I got theta=tantheta when horizontal tangent occur
and theta=cotangent theta when vertical tangent occur. Then How to calculate them?[/quote]

correction ... horizontal tangent occurs when $\theta = -\tan{\theta}$

have to solve these with a calculator.

**dylan5188** · March 23rd 2010, 07:33 PM

Still dont know how to calculate

**skeeter** · March 24th 2010, 07:01 AM

Originally Posted by dylan5188

Still dont know how to calculate

graph the equation $y = x + \tan{x}$ with your graphing calculator and look for the zeros between $0$ and $2\pi$

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