1. What is Tangent?

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. It's a fundamental trigonometric function used in mathematics, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the tangent formula:

Where:

• \( \theta \) — Angle in the right triangle
• opposite — Length of the side opposite to the angle
• adjacent — Length of the side adjacent to the angle

Explanation: The tangent function relates the ratio of two sides of a right triangle to one of its non-right angles.

3. Importance of Tangent Calculation

Details: Tangent is essential for solving problems involving right triangles, calculating slopes, and in various applications like navigation, engineering, and physics.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of tangent values?
A: Tangent values range from negative infinity to positive infinity, depending on the angle.

Q2: What happens when the adjacent side is zero?
A: When adjacent side approaches zero, the tangent approaches infinity (undefined at exactly 90 degrees).

Q3: How is tangent different from sine and cosine?
A: While sine is opposite/hypotenuse and cosine is adjacent/hypotenuse, tangent is opposite/adjacent.

Q4: Can tangent be negative?
A: Yes, tangent is negative in the second and fourth quadrants of the unit circle.

Q5: What are practical applications of tangent?
A: Used in calculating heights of buildings, angles of elevation/depression, and in computer graphics.