Convertong polar equations to rectangular eq.

In summary, the conversation is about finding the value of theta, which is equal to 45 degrees. The relevant equations are provided, which state that when x is positive or negative, theta is equal to the arctan of y/x. The attempt at a solution involves using the equation Tan(45)=y/x and solving for y, which results in y=x. The conversation concludes with a clarification that the line y=x does indeed make a 45 degree angle with the positive x-axis.
  • #1
catteyes
9
0

Homework Statement


(theta)= 45Degrees


Homework Equations


(theta)= Arctan(y/x) (x>0)
(theta)= Arctan(y/x) (x<0)


The Attempt at a Solution



Tan(45)=y/x
1 = y/x
Does that mean Y = X?
:confused:
 
Physics news on Phys.org
  • #2
catteyes said:

Homework Statement


(theta)= 45Degrees


Homework Equations


(theta)= Arctan(y/x) (x>0)
(theta)= Arctan(y/x) (x<0)


The Attempt at a Solution



Tan(45)=y/x
1 = y/x
Does that mean Y = X?
:confused:
Yes, it does! If you are not convinced, draw an xy- coordinate system, mark the line at 45 degrees to the positive x-axis and draw the line y= x!
 
  • #3
What angle to the positive x-axis does the line y=x make?
 
  • #4
oh 45 degrees.

thanks
 

Related to Convertong polar equations to rectangular eq.

1. What is the process for converting a polar equation to a rectangular equation?

The process for converting a polar equation to a rectangular equation involves using the following formulas:

x = r*cos(theta)

y = r*sin(theta)

Where r is the distance from the origin and theta is the angle measured from the positive x-axis.

2. Can all polar equations be converted to rectangular equations?

Yes, all polar equations can be converted to rectangular equations using the above formulas.

3. How do I know if a polar equation is symmetric about the x-axis or y-axis?

A polar equation is symmetric about the x-axis if it is unchanged when theta is replaced by -theta. It is symmetric about the y-axis if it is unchanged when theta is replaced by theta +/- 180 degrees.

4. Are there any special cases when converting polar equations to rectangular equations?

Yes, when converting a polar equation to a rectangular equation, you may encounter special cases such as when the polar equation contains the form r = a + b*cos(theta) or r = a + b*sin(theta). In these cases, additional steps may be required to convert the equation to rectangular form.

5. Is there a way to graph a polar equation after converting it to rectangular form?

Yes, after converting a polar equation to rectangular form, you can graph it by plotting the x and y coordinates obtained from the conversion. This will result in a graph in the Cartesian coordinate system.

Similar threads

Polar equation to rectangular equation
    • Precalculus Mathematics Homework Help
Replies
11
Views
1K
Line passing through the origin (polar coordinates)
    • Precalculus Mathematics Homework Help
Replies
11
Views
2K
Question about arctan addition
    • Precalculus Mathematics Homework Help
Replies
17
Views
2K
Solving an equation for ##x## involving inverse circular functions
    • Precalculus Mathematics Homework Help
Replies
15
Views
1K
Exploring Equation of a Straight Line in 3D Space
    • Precalculus Mathematics Homework Help
Replies
17
Views
1K
I How to apply tensor transformation rule
    • Differential Geometry
Replies
9
Views
427
State the domain and range for a given function
    • Precalculus Mathematics Homework Help
Replies
7
Views
426
How Do You Determine the Polar Equation of a Line Perpendicular to a Given Ray?
    • Precalculus Mathematics Homework Help
Replies
6
Views
1K
Asymptote of a curve in polar coordinates
    • Precalculus Mathematics Homework Help
Replies
6
Views
4K
Show that the ratio ##x+y:x-y## is increased by subtracting ##y##
    • Precalculus Mathematics Homework Help
Replies
4
Views
666

Hot Threads

Recent Insights

Back
Top