Write out the polar coordinate equation of Archimedes spiral and draw the figure

When a point P moves along the moving ray OP at the same speed, the ray rotates around the point o at the same angular speed. The trajectory of point P is called Archimedes spiral. Its polar coordinate equation is: R & nbsp; = & nbsp; a θ & nbsp; & nbsp; & nbsp; & nbsp; the distance of each arm of the spiral is always equal to & nbsp; 2 π a

Write out the polar coordinates of a, B, C, D, e, F and G (ρ > 0,0 ≤ θ)

A (3,0)... B (2, Pie / 4), C (3, Pie / 2) d (1,5 Pie / 6)
E (2.5, - Pie), f (5, - 2 Pie / 3), G (4, - Pie / 3)

Polar coordinates: P = radical 2 * SiNx (x from 0 to 2)
Where is the center of the circle?
What is the polar equation of a circle? How did you get here
Who has this knowledge? Let me have a look~

Transformation of Cartesian coordinates and polar coordinates:
ρ^2=x^2+y^2
ρsinθ=y
ρcosθ=x
Multiply both sides of ρ = √ 2 * sin θ by ρ to get ρ ^ 2 = √ 2 * ρ sin θ
So x ^ 2 + y ^ 2 = √ 2Y
That is: x ^ 2 + y ^ 2 - √ 2Y = 0
x^2+(y-√2/2)^2=1/2
So the center of the circle is (0, √ 2 / 2)

Cartesian cardioid r = a (1-sinx)
If you know something about polar coordinates, what value should a be brought into this equation? Variables?
When drawing, what is brought in by method X?

Here, a is a constant, which determines the size of the cardioid pattern, so it doesn't matter what number it takes. The so-called x is the angle between the polar diameter and the polar axis. Therefore, the value range is 0-2pi, and R is the polar diameter. As shown in the figure, this is r = a (1 + cosx)

A point on a number axis that represents an integer is called an integral point. The unit length of a certain number axis is 1cm. If you draw a line AB with a length of 1000cm on the number axis at will
Then the number of integral points covered by line AB is?

A point on the number axis that represents an integer is called an integral point
The unit length of a number axis is 1cm
If a 2011cm long line AB is drawn randomly on this axis
Then the number of integral points covered by line AB is (2011 or 2012)

Draw a line ab of 1000 cm on the number axis in unit length 1, and find the number of integers covered by line ab

1000

If a line AB with length of 2009cm is drawn randomly on the number axis with unit length of 1cm, then the integral points covered by line AB have at least ()
A. 2007 b.2008 c.2009 d.2010

There are two cases
1. A and B are on the whole. The answer is 2010
2. A and B are not on the whole. The answer is 2009

A point on a number axis that represents an integer is called an integral point. The unit length of a certain number axis is 1cm. If you draw a line ab of 2000cm at will on this number axis
Then the point covered by line AB is
A. 1998 or 1999 B, 1999 or 2000
C. 2000 or 2001 D, 2001 or 2002

If the electron ant P starts from point B and moves to the left at the speed of 6 unit lengths per second, and the other electron ant Q starts from point a and moves to the left at the speed of 4 unit lengths per second
Let two electronic ants meet at point D on the number axis. Do you know the number corresponding to point d? (the number corresponding to point a is - 20, and the number corresponding to point B is 100)

120 / 2 = 60 seconds. It takes 60 seconds for P to meet Q. 4 * 60 = 240, - 20-240 = - 260, and the corresponding number of D is - 260

If when the electronic ant P starts from point B, if the electronic ant P starts from point B, it moves to the left at a speed of 3 units per second, and the other electronic ant Q just starts
If the electronic ant P starts from point B and moves to the left at the speed of 3 units / second, and the other electronic ant Q just starts from point a and moves to the right at the speed of 2 units / second, how long does it take for the two ants to be 35 units apart on the number axis?
Point B is 90, point a is - 10!

Suppose: ant P starts from point B to the left, ant Q starts from point a to the right, the trajectory of the movement is on the number axis, and it is a straight line movement. Sub situation discussion: 1. If two points a and B coincide, then: P moves from a to the left at a speed of 3 U / s, Q moves from B to the left at a speed of 2 U / s

Write out the polar coordinate equation of Archimedes spiral and draw the figure