Madeira Precalculus Blog: Precalculus 4/12/2010

Monday, April 12, 2010

Precalculus 4/12/2010

Polar coordinates - day 1

Formulas:

$sin(\theta)=\frac{y}{r}$

$cos(\theta)=\frac{x}{r}$

$r*sin(\theta)=y$

$r*cos(\theta)=x$

Example #1

finding polar coordinates

$(r,\theta)$

$(2,\frac{\pi}{3})$

Find another part that r is negative:

Theta has to be greater than pi, and less than 2pi.

In order for that to happen you need to make the radius negative

$(\pi<\theta<2\pi) = (-2,\frac{4\pi}{3})$

when r is positive:

Theta has to be greater than -2pi and less than zero.

so you need to make theta negative for this one to work.

$(-2\pi<\theta<0) = (2,-\frac{5\pi}{3})$

Example #2

Convert from Polar to Rectangular

use the equations given earlier

$(4,\frac{\pi}{2})$

$4*cos\frac{\pi}{2}=x$

and the cosine of pi/2 is 0 so...

next you find y.

$4*sin\frac{\pi}{2}=y$

and the sine of pi/2 is 1 so...

So the point in rectangular form is (0,4)

Example #3

Converting from Rectangular to Polar

use the formulas provided above

Convert the point (-1,1)

Find r:

$2=r^2,~\sqrt{2}=r$

Find theta:

$(\theta)=tan^-1({-1})$

$=\frac{3\pi}{4},\frac{7\pi}{4}$

so you are left with the point:

$(\sqrt{2},\frac{3\pi}{4})$

If you need more help you can go to Mr.Corn's website: http://web.mac.com/jeffcorn/iweb

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