Thread: Polar Equation: Draw and Fill in chart

Draw and fill in the chart that has a row for "Theta" and a row for "r" for this polar equation: r=1-3cos(theta)

I have to fill in the 24 spots (12 for theta and 12 for r) on the chart using this polar equation: r=1-3cos(theta).

The picture given is a unit circle counting by pi/12. Please help???

Hve you been introduced to ...polar plot r=1-3cos(t) - Wolfram|Alpha ?

Thank you very much. How would I go about solving for R when cos(theta)= pi/12?

Originally Posted by Binary

Thank you very much. How would I go about solving for R when cos(theta)= pi/12?

I think you mean ... "how can I evaluate $\displaystyle r$ when $\displaystyle \theta = \frac{\pi}{12}$" ?

$\displaystyle r = 1 - 3\cos\left(\frac{\pi}{12}\right)$

... get out your calculator

$\displaystyle r \approx 0.966$


by hand ...

$\displaystyle \cos\left(\frac{\pi}{12}\right) = \cos\left(\frac{\pi}{3} - \frac{\pi}{4}\right)$

... use the difference identity for cosine.

Originally Posted by skeeter

I think you mean ... "how can I evaluate $\displaystyle r$ when $\displaystyle \theta = \frac{\pi}{12}$" ?

$\displaystyle r = 1 - 3\cos\left(\frac{\pi}{12}\right)$

... get out your calculator

$\displaystyle r \approx 0.966$


by hand ...

$\displaystyle \cos\left(\frac{\pi}{12}\right) = \cos\left(\frac{\pi}{3} - \frac{\pi}{4}\right)$

... use the difference identity for cosine.

Yeah I figured it out finally then just saw your post. Thank you very much. I was trying to do it by hand btw.

When I use my calculator I dont get r=0.966. I get approx r=-1.897

Originally Posted by Binary

When I use my calculator I dont get r=0.966. I get approx r=-1.897

you're correct ... I only punched in $\displaystyle \cos\left(\frac{\pi}{12}\right)$ , my mistake.