change (2,2)to polar coordinate i need to know how to do it?

Answer 1

'x= rcost
y=rsint

and r= sqrt(x^2+y^2)
t=arctan(y/x)
so
if x=2, and y=2, then r= sqrqt(4+4)=sqrt(8)
and t=arctan(2/2) = arctan(1) = pi/4

Answer 2

Think of a right triangle, formed by starting at the origin and going 2 spaces right then 2 spaces up. You could get to that same place by going on a straight line from the origin to the point (2,2). The distance you would travel on that straight line would be found by using the Pythagorean theorem.

√(2^2+2^2) = √(8) = 2√(2)

Now you need to find the angle that you are traveling. You do this by finding the inverse tangent of the opposite side over the adjacent side, in this case arctan(2/2) = arctan(1) = 45º

So the polar form is 2√(2)<45º also written (2√(2),45º).

(I'm using < for the angle sign.)

Answer 3

To convert orthogonal coordinates to polar coordinates, you must use trigonometry thus:

Imagine a right triangle with one point at the center of the graph (0,0). One side of the triangle runs from that point due east or west, along the X axis, to a point on that axis due north or south of the point you're converting. In this case, that point is (2,0).

The second side of the triangle is from that point up or down to the point you're converting. In this case, that's (2,2). The angle that you just turned to make this second line is the right angle in the right triangle.

The third side of the triangle is the hypotenuse and it runs back to (0,0).

Using the Pythagorean theorem, you can find the length of the hypotenuse, about 2.828 in this case. That is equal to the radius part of the polar coordinates. Now to find the angle.

Remembering the triangle you have imagined, find the sine and cosine of the angle formed by the line extending due east (the X axis) and the hypotenuse of your triangle. Since the point is in the northeast quadrant, both numbers will be positive. The sine is the length of the triangle's distant leg - the vertical line - divided by that of the hypotenuse; the cosine is the length of the close leg - the horizontal line - divided by that of the hypotenuse.

In your case, both of the short sides of the triangle are equal, so sine and cosine are also equal, they are about 0.707. The sine divided by the cosine (in this case, 1) is the tangent, and the inverse tangent is the angle part of the polar coordinates. The inverse tangent of 1 is 45 degrees.

Depending on which quadrant the point is in, you sometimes have to adjust this number (the signs of the sine and cosine will tell you if this is necessary.)

So, the converted point in polar is (45deg, 2.828).

Answer 4

The other answers show the math, so I'll take a stab at the concept. The idea with polar coordinates is to describe a line between the origin (0,0) and your point (2,2). The line gets described by how long it is, and the angle off the positive X-axis ( the one going ---->). (2,2) is a good'un to start with since it is an easy angle to figgure out, and an easy length. Picture it as a triangle where both sides are 2 long. All you need to do is figgure out the hypotenuse and the angle. Just looking at it you know the angle is going to be 45, and you know from thrid grade how to figgure out the hypotenuse.

hope this helps

Answer 5

The previous answer confused me, and I used to teach math.

Picture (2,2) on a coordinate system. Instead of (x,y) you want (r,theta), where r is the distance from the origin (0,0) and theta is the angle measured from the positive x-axis.

(0,0) and (2,2) form a 45-45-90 right triangle. r is the hypotenuse which equals 2 sqrt 2. Theta is 45 degrees, or pi/4. Therefore, the coordinates are:

(2 sqrt 2, pi/4)

Answer 6

Polar coordinates are
r = sqrt(x^2 + y^2)
and theta = arctan(y/x)
[i.e. tan(theta) = y/x]

This should give you
r = 2*sqrt(2), Theta = 45 deg. Check it.