Enter the radius and angle in degrees into the calculator to determine the slope of a curve in polar coordinates.
Polar Slope Formula
The following formula is used to calculate the slope of a curve in polar coordinates.
dy/dx = tan(θ) + θ / r
Variables:
- dy/dx is the slope of the curve in polar coordinates
- θ is the angle in radians
- r is the radius
To calculate the slope of a curve in polar coordinates, use the tangent of the angle plus the angle divided by the radius.
What is Polar Slope?
Polar slope refers to the steepness or incline of a curve at a particular point in polar coordinates. Unlike Cartesian coordinates where the slope is the ratio of the change in y to the change in x, the slope in polar coordinates takes into account the radial distance from the origin and the angle with respect to the positive x-axis. It is a crucial concept in fields such as physics, engineering, and mathematics, especially when dealing with circular or spiral phenomena.
How to Calculate Polar Slope?
The following steps outline how to calculate the Polar Slope.
- First, determine the radius (r) of the curve at the point of interest.
- Next, determine the angle (θ) at the point of interest, in degrees.
- Convert the angle from degrees to radians by multiplying by π/180.
- Use the formula from above to calculate the slope (dy/dx).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
radius (r) = 5
angle (θ) = 30 degrees
