Finding the Coordinates of a Point Using Rectangular and Polar Formulas

In summary, to determine the value of r and y for a point given its rectangular coordinates and polar coordinates, you can use the equations r = sqrt(x^2 + y^2) and theta = arctan(y/x) to solve for r and y. Alternatively, you can use the equations x = rcos(theta) and y = rsin(theta) to solve for r and y.
  • #1
ArcadianGenesis
8
0

Homework Statement



The rectangular and polar coordinates of a point are (x,y) and (r,theta) where x = 7 and theta = 52 degrees. Determine r and y.

Homework Equations



r = srt(x^2 + y^2)
theta = arctan(y/x)
x = rcos(theta)
y = rsin(theta)

The Attempt at a Solution



I tried to assume that r and x would be the same, so I let r = 7, which would then make y = 5.5. But that's wrong. What else can possibly be done?
 
Last edited:
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  • #2
2 equations, 2 unknowns

Use:
x=rcos(theta) eqn. 1
y=rsin(theta) eqn. 2

Since you know what x and theta are you can solve for r in eqn. 1.

Then once you know r you can plug that into eqn. 2 and solve for y.
 
  • #3
Haha, nice. I was having one of those mental blocks that just would not allow me to think of that. Thanks.
 

FAQ: Finding the Coordinates of a Point Using Rectangular and Polar Formulas

1. What are coordinates in physics?

Coordinates in physics refer to a system of numbers and symbols used to describe the location of an object in space. They are typically represented by x, y, and z axes, and can also include time.

2. Why are coordinates important in physics?

Coordinates are important in physics because they allow us to precisely describe the position, velocity, and acceleration of objects in space. They also enable us to make predictions and calculations about the motion of objects.

3. How are coordinates used in physics equations?

Coordinates are used in physics equations to represent the position, velocity, and acceleration of objects. They are typically used in conjunction with other variables, such as time, to describe the motion of objects.

4. What is the difference between Cartesian and polar coordinates in physics?

Cartesian coordinates, also known as rectangular coordinates, use x, y, and z axes to describe the position of an object in space. Polar coordinates, on the other hand, use a radius and angle to describe the position of an object relative to a fixed point.

5. How do you convert between Cartesian and polar coordinates in physics?

To convert between Cartesian and polar coordinates, you can use the following equations:

x = r cos(θ)

y = r sin(θ)

where r is the radius and θ is the angle in polar coordinates, and x and y are the coordinates in Cartesian form. These equations can be used to convert coordinates in either direction.

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