i am stupid...please help me!!!?

Question

identify, by name, each polar graph.give at least one characteristic of each graph.
1. r=2
2. r=3sec(theta)
3. r=1+sin(theta)
4. r=2cos 3(theta)

Answer 1

#1 The first is a circle of radius 2. This is because if a figure has a fixed radius (r), then it is a circle.

http://math.colgate.edu/~kellen/interspace/r1.gif

#2 The second is a line x=3. Why? Remember, there is a right triangle with legs x,y and hypotenuse r.

r = √(x² + y²)
tan(Θ) = y/x
sec(Θ) = r / x

So our equation becomes:

r = 3 sec(Θ) = 3r/x
rx = 3r
x = 3

http://math.colgate.edu/~kellen/interspace/r2.gif

#3 The third one is called a cardioid. It is a classic polar graph, and is well known to mathematicians.

http://en.wikipedia.org/wiki/Cardioid
http://math.colgate.edu/~kellen/interspace/r3.gif

#4 The last is called a "rose" because it resembles a flower. It loops around three times before repeating, due to the 3 in the cosine. It also has "radius" 2 (meaning it fits inside a circle of radius 2).

http://en.wikipedia.org/wiki/Rose_%28mathematics%29
http://math.colgate.edu/~kellen/interspace/r4.gif

Answer 2

1. A circle with radius 2 centered at the origin
2. A vertical line at x = 3 in the x-y coordinates plane
3. A heart shaped curve with y as the symmetry axis
4. It is probably called 3-patel rose leaf with max along theta = 0, 2pi/3, and 4pi/3