1. What is Slope?

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change to the horizontal change between two points on the line. When you have the angle of the line from the horizontal axis, the slope is the tangent of that angle.

2. How Does the Calculator Work?

The calculator uses the trigonometric tangent function:

Where:

• \( \theta \) — Angle from the horizontal axis (degrees)
• \( \tan \) — Trigonometric tangent function

Explanation: The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side, which corresponds to the slope of the line.

3. Importance of Slope Calculation

Details: Slope calculation is fundamental in mathematics, physics, engineering, and many other fields. It helps determine rates of change, gradients, and inclines in various applications.

4. Using the Calculator

Tips: Enter the angle in degrees (between -90° and 90°). The calculator will compute the slope as the tangent of that angle.

5. Frequently Asked Questions (FAQ)

Q1: What does a slope of 1 mean?
A: A slope of 1 means the line rises 1 unit for every 1 unit of horizontal distance (45° angle).

Q2: What does a negative slope indicate?
A: A negative slope means the line is decreasing as you move from left to right (negative angle).

Q3: What's the slope of a vertical line?
A: A vertical line has an undefined slope (90° angle), as tan(90°) is undefined.

Q4: How does slope relate to derivatives?
A: The derivative of a function at a point gives the slope of the tangent line to the function at that point.

Q5: What's the maximum possible slope value?
A: As the angle approaches 90°, the slope approaches infinity. There is no maximum finite slope value.