1. What is the Tangent Function?

Definition: The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

Purpose: It's a fundamental trigonometric function used in mathematics, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \tan(\theta) \) — Tangent of angle θ (dimensionless)
• \( \sin(\theta) \) — Sine of angle θ
• \( \cos(\theta) \) — Cosine of angle θ
• \( \theta \) — Angle in degrees (0° to 360°)

Explanation: The calculator converts the angle to radians, then calculates sine and cosine to compute the tangent ratio.

3. Importance of Tangent Function

Details: The tangent function is crucial for solving problems involving slopes, angles of elevation/depression, and periodic phenomena.

4. Using the Calculator

Tips: Enter any angle between 0° and 360° to calculate its tangent value along with its sine and cosine components.

5. Frequently Asked Questions (FAQ)

Q1: Why does tangent approach infinity at 90°?
A: At 90°, cosine is 0, making the denominator 0 in the tangent formula, which is undefined (approaches infinity).

Q2: What's the period of the tangent function?
A: The tangent function has a period of 180° (π radians), repeating every half rotation.

Q3: How is tangent used in real-world applications?
A: It's used in calculating slopes, roof pitches, navigation, and in physics for analyzing forces and motion.

Q4: What's the relationship between tangent and other trig functions?
A: Tangent is also equal to sine divided by cosine, and is the reciprocal of cotangent.

Q5: Why do we sometimes get very large tangent values?
A: As cosine approaches zero (near 90° and 270°), tangent values become extremely large in magnitude.