how do I graph r = 2costheta on an x-y plane?

Question

can anyone help me graph r = 2costheta on an x-y plane. please show me what you did step by step.thank you

the graph doesnt look like a cosine curve, it should look more like a circle since it is a polar equation but I dont know how to draw it and how to come up with points

Answer 1

Chimp, for your easy graphing, know that

r = a cos theta is the standard graph of a circle with center (a/2, 0) and radius Ia/2I.

examples: r = 3 cos theta is a circle radius 1.5, center (1.5, 0)
r = 6 cos theta is a circle center (3, 0) radius 3
r = - 4cos theta is a circle center (-2, 0) radius 2.

If you have r = a sin theta instead, the center will be on y-axis instead of x-axis.
Center (0, a/2) radius Ia/2I
example:
r = 12sin theta is a circle radius 6, center (0, 6)
r = - 6 sin theta is a circle radius 3 center (0, -3)

Answer 2

r = 2cos (theta)

is the regular cosine curve after a vertical expansion by a factor of 2.

So, draw y = cos(theta)

The new graph will have the same x-intercepts as this graph

All other points will become two times further away from the x-axis. For example, the 'high points' will be at y = 2 instead of the original y = 1, and the 'lowest points' will be at y = -2 instead of the original y = 1. The x-values for these points will not change.

Answer 3

The graph is a circle with radius 2/2 = 1. The center is at the point (x,y) = (1,0). It goes thru the origin.

Answer 4

I admit that i'm slightly puzzled by ability of your question. it fairly relies upon on despite the fact that if the quantity is by using this section initiate grew to become around with regard to the x-axis or the y-axis. First, discover the coordinates of the factors of intersection of the two equations. y=x and y=x^2 x = x^2 x^2 - x = 0 x(x - a million) = 0 x = 0 and x-a million = 0 x = 0 and a million while x = 0, y = 0 => (0,0) while x = a million, y = a million => (a million,a million) combine pi*(x-x^2)^2 with comprehend to x from 0 to a million, as we are rotating the form with regard to the x-axis. next, boost the fundamental. Integration of pi*(x^2 - 2x^3 + x^4) from 0 to a million consequence pi*[(a million/3)x^3 - (2/4)x^4 + (a million/5)x^5] from 0 to a million = pi*[a million/3 - a million/2 + a million/5] - pi*[0] = pi*[-a million/6 + a million/5] = pi*[a million/30] = (a million/30)pi