Could you please tell me how to plot r=2cos theta ? Please show me the step of plotting this graph. Thanking in advance.
Decide on a set of $\displaystyle \theta$ values, say,
$\displaystyle \theta = 0, \pi/4, \pi/2, 3\pi/4, pi, 5pi/4, 3\pi/2, 7\pi/4$ rad
Then calculate the r value for each $\displaystyle \theta$. They are
$\displaystyle r = 2, \sqrt{2}, 0, -sqrt{2}, -2, -\sqrt{2}, 0, \sqrt{2}$ (respectively)
What do you do with negative r values? Well, you make the r value positive and then add (or subtract) $\displaystyle \pi$ rad to the angle.
So we wish to plot the set of points:
$\displaystyle (r, \theta)$
$\displaystyle (2, 0)$
$\displaystyle (\sqrt{2}, \pi/4)$
$\displaystyle (0, \pi/2)$
$\displaystyle (\sqrt{2}, 5\pi/4)$
$\displaystyle (2, 0)$ <-- $\displaystyle \pi + \pi = 2\pi \to 0$
$\displaystyle (\sqrt{2}, \pi/4)$
$\displaystyle (0, 3\pi/2)$
$\displaystyle (\sqrt{2}, 7\pi/2)$
Then you plot the points on polar coordinate graph paper and sketch in a smooth curve between the points. I get the graph below.
-Dan
Or you could do it the hard way:
$\displaystyle r = \sqrt{x^2 + y^2}$
$\displaystyle cos(\theta) = \frac{x}{\sqrt{x^2 + y^2}}$
So your equation becomes:
$\displaystyle \sqrt{x^2 + y^2} = 2 \frac{x}{\sqrt{x^2 + y^2}}$
Multiplying both sides by $\displaystyle \sqrt{x^2 + y^2}$ gives:
$\displaystyle x^2 + y^2 = 2x$
$\displaystyle (x^2 - 2x) + y^2 = 0$
$\displaystyle (x^2 - 2x + 1) + y^2 = 1$
$\displaystyle (x - 1)^2 + y^2 = 1$
which is a circle centered on (1, 0) with radius 1.
-Dan