In polar coordinates, P = 4sin @ is the polar equation of a circle, then the distance from a (4, Wu / 4) to the center of the circle C is----

Round to rectangular coordinates, the equation is x ^ 2 + (Y-2) ^ 2 = 4, point a (2 root sign 2, 2 root sign 2), so the distance = root sign (20-8 root sign 2)

How can rectangular coordinates of a circle be transformed into polar coordinates

X is replaced by ρ cos θ and y by P sin θ

What is the polar equation of the ball?

In mathematics, the polar coordinate system is a two-dimensional coordinate system. The point in the coordinate system is represented by an angle and a distance from the relative center point, the pole (equivalent to the origin in the rectangular coordinate system). The polar coordinate system has a wide range of applications, It includes the fields of mathematics, physics, engineering, navigation and robotics. When the relationship between two points is easily expressed by angle and distance, polar coordinate system is particularly useful; while in the plane rectangular coordinate system, such relationship can only be expressed by trigonometric function. For many types of curves, polar coordinate equation is the simplest expression, even for some curves, Only the polar equation can be expressed
A point P represented by spherical coordinates
Spherical coordinate system can also be extended into three dimensions by using coordinates (ρ, φ, θ), where ρ is the distance from the center of the ball, φ is the angle from the Z axis (called the co latitude or vertex angle, from 0 to 180 °), and θ is the angle from the X axis (as in polar coordinates). This coordinate system is called spherical coordinate system, similar to the longitude and latitude used for the earth, latitude is the co angle, depending on δ = 90 ° - φ, Longitude can be calculated by L = θ - 180 degree
Through the following formula, the spherical coordinates can be expressed in rectangular coordinates. The following website is the calculation process of the polar equation of the ball, which has a very detailed description. It is recommended to use Google browser to translate it into Chinese directly, so that it is easy to understand

How does the polar coordinate of the central line change into a rectangular coordinate system equation?

Cardioid ρ = a (1-cos θ),
Multiply both sides by ρ, and you get
ρ^2+aρcosθ=aρ,
Let x ^ 2 + y ^ 2 + AX = a √ (x ^ 2 + y ^ 2)

A point on the number axis represents a number. When the number represented by this point is an integer, we call it an integral point. If there is a caterpillar team with a length of 2009cm, which is connected end to end, crawling along the number axis, how many integral points does the team cover in the process of crawling?

When the head and tail of the caterpillar team are just on the whole point, the whole point covered by the caterpillar team is 2009 + 1 = 2010;
When the head and tail of the caterpillar team are not on the whole point, the whole point covered by the caterpillar team is 2009-1 = 2008
Therefore, the caterpillar team covers 2010 or 2008 whole points

Inspired by the production of fried dough sticks, Mr. Li designed a mathematical problem. He intercepted the line AB from the origin to the corresponding point of 1 on the number axis, folded it in half (point a and B coincide) and then evenly pulled it into a line segment of unit length. This process is called one operation (for example, after the first operation, 1 / 4, 3 / 4 on the original line AB become 1 / 2, 1 / 2 become 1, etc.), After the third operation, what is the sum of the numbers corresponding to the point where 1 coincides?... tell us the speed

It was 1 before the operation
1 / 2 after the first operation
1 / 4 and 3 / 4 after the second operation
After the third operation, there are 1 / 8 and / 3 / 8 and 5 / 8 and 7 / 8, so the sum is 2
(Supplement)
There's nothing to tangle with. I know that the best answer is chosen by the questioner. There is no objective judgment, so the questioner thinks that the answer is right, but it's actually wrong. If you look at the relevant links of this question, most of them are right

Inspired by the production of ramen, Mr. Chen intercepted the line AB from the origin to the corresponding point of 1 on the number axis, folded it in half (points a and B coincide) and then evenly pulled it into a line segment of unit length. This process is called one operation (for example, after the first operation, one quarter and three quarters of the original line AB become one half, and one half becomes one, etc.), The number corresponding to the point exactly pulled to coincide with 1 is——

Solution: according to the meaning of the question, the number corresponding to the point which coincides with 1 after the first operation is 1 * 1 / 2 = 1 / 2, the number corresponding to the point which coincides with 1 after the second operation is 1 / 2 * 1 / 2 = 1 / 4 = 1 / (2 ^ 2), and the number corresponding to the point which coincides with 1 after the third operation is 1 / 4

Inspired by the production of ramen, Mr. Li designed a mathematical problem: as shown in the figure, cut the line AB from the origin to the corresponding point of 1 on the number axis, fold it in half (point a and B coincide) and then evenly pull it into a line segment of unit length. This process is called one operation (for example, after the first operation, 14 and 34 on the original line AB become 12, 12 become 1, etc.) In the points above (except a and b), after the second operation, the sum of the numbers corresponding to the points pulled to coincide with 1 is___ ．

∵ after the first operation, the corresponding points of 14 and 34 on the original line AB all become 12, and the corresponding points are expanded by 2 times. Then, after the second operation, the corresponding numbers of the points that are pulled to coincide with 1 are 14 and 34, so the sum of them is 1

With the length of 2011 unit length line AB on the number axis, can cover up to - integer points

Using line ab of 2011 unit length on the number axis can cover up to 2012 integer points

A point representing an integer on a number axis is called an integral point. The unit length of a certain number axis is 1 cm. If a line segment AB with a length of 2000 cm is randomly drawn on this number axis, how many lines are covered by the line segment AB?
A 1998 or 1999 B 1999 or 2000 C 2000 or 2001 D 2001 or 2002
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In polar coordinates, P = 4sin @ is the polar equation of a circle, then the distance from a (4, Wu / 4) to the center of the circle C is----