How do you find the maximum R value?

The maximum value of r=2+2cosθ occurs when cosθ is a maximum, which is when cosθ=1 or when θ=0. Substitute θ=0 into the equation, and solve for r.

How do you draw polar graphs?

to graph a point on the polar plane, you should find theta first and then locate r on that line. This approach allows you to narrow the location of a point to somewhere on one of the lines representing the angle. From there, you can simply count out from the pole the radial distance.

What is 2 cos theta?

Cosine 2 theta is 1 minus 2 sine squared theta, cosine 2 theta equals 2 cosine squared minus 1.

How do you find cos 2 theta?

The cosine double angle formula is cos(2theta)=cos2(theta) – sin2(theta). Combining this formula with the Pythagorean Identity, cos2(theta) + sin2(theta)=1, two other forms appear: cos(2theta)=2cos2(theta)-1 and cos(2theta)=1-2sin2(theta).

What is the equation for R=cos2theta in polar coordinates?

The equation r=cos2theta is in polar coordinates. When theta=0,pi/2,pi, (3pi)/2,2pi, we have r=1 and when theta=pi/4, (3pi)/4, (5pi)/4, (7pi)/4, we have r=0 Hence, the courve moves from r=1 at theta=0 to r=0 at theta=pi/4 to r=1 at theta=pi/2.

How do you graph a polar equation?

Graphing a polar equation is accomplished in pretty much the same manner as rectangular equations are graphed. They can be graphed by point-plotting, using the trigonometric functions period, and using the equation’s symmetry (if any).

Why is R=cos2theta called a rose curve?

The equation r=cos2theta is in polar coordinates. Hence, the courve moves from r=1 at theta=0 to r=0 at theta=pi/4 to r=1 at theta=pi/2. Note that in between at theta=pi/6 we have r=1/2 and so on forming four petals. That is why it is called rose curve as well.

How do you prove a graph is symmetric with respect to?

Replace θ with -θ. If an equivalent equation results, the graph is symmetric with respect to the polar axis. Replace θ with -θ and r with -r. If an equivalent equation results, the graph is symmetric with respect to θπ=. 2