Polar Curve Angle Calculator

Polar Curve Angle Formula:

\[ \theta = \arctan\left(\frac{dy}{dx}\right) \]

Calculated Angle:

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1. What is the Polar Curve Angle?

The polar curve angle represents the angle between the tangent to a curve at a given point and the positive x-axis. It's calculated using the derivative of the curve function at that point.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

\[ \theta = \arctan\left(\frac{dy}{dx}\right) \]

Where:

\( dy \) — Change in the y-direction
\( dx \) — Change in the x-direction
\( \theta \) — Resulting angle in degrees

Explanation: The arctangent function calculates the angle whose tangent is the ratio of dy to dx, giving the slope angle of the curve.

3. Importance of Angle Calculation

Details: Calculating the angle of a curve is essential in various fields including physics, engineering, and computer graphics for determining direction, slope, and orientation of moving objects or surfaces.

4. Using the Calculator

Tips: Enter the change in y (dy) and change in x (dx) values. The dx value cannot be zero as division by zero is undefined. Results are provided in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What if dx is zero?
A: When dx is zero, the slope is vertical, and the angle is undefined (or considered 90 degrees in some contexts).

Q2: How is the result converted to degrees?
A: The calculator first computes the angle in radians using the arctan function, then converts it to degrees using the rad2deg conversion.

Q3: Can this calculator handle negative values?
A: Yes, the calculator can process negative dy or dx values, which will result in angles in different quadrants.

Q4: What's the range of output angles?
A: The output angles range from -90° to 90°, covering all four quadrants based on the signs of dy and dx.

Q5: How precise are the results?
A: Results are calculated with high precision and rounded to two decimal places for readability.