1. What is the Tangent Function?

The tangent function is a fundamental trigonometric function that relates the ratio of the opposite side to the adjacent side in a right-angled triangle. It's periodic with period π and has asymptotes where cosine equals zero.

2. How Does the Calculator Work?

The calculator uses the tangent function:

Where:

• \( x \) — Angle in radians
• \( \sin(x) \) — Sine of angle x
• \( \cos(x) \) — Cosine of angle x

Explanation: The tangent function is undefined when cos(x) = 0 (at odd multiples of π/2).

3. Importance of Tangent Calculation

Details: Tangent is widely used in mathematics, physics, engineering, and computer graphics for solving problems involving angles and slopes.

4. Using the Calculator

Tips: Enter angle in radians (for degrees, convert first: radians = degrees × π/180). The calculator will return the tangent value.

5. Frequently Asked Questions (FAQ)

Q1: Why does my calculator return strange values for certain angles?
A: This happens at angles where cosine is zero (like π/2, 3π/2). The tangent function approaches infinity at these points.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533).

Q3: What's the range of the tangent function?
A: The range is all real numbers (-∞, +∞).

Q4: Is tangent periodic?
A: Yes, with period π (180°), unlike sine and cosine which have period 2π.

Q5: What are some practical applications of tangent?
A: Calculating slopes, angles of elevation/depression, in navigation, and in Fourier analysis.