1. What is the Tangent Function?

The tangent function is a fundamental trigonometric ratio that relates the opposite side to the adjacent side of a right-angled triangle. It's one of the three primary trigonometric functions along with sine and cosine.

2. How Does the Calculator Work?

The calculator uses the tangent formula:

Where:

• opposite — Length of the side opposite to the angle
• adjacent — Length of the side adjacent to the angle

Explanation: 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.

3. Importance of Tangent Calculation

Details: The tangent function is widely used in mathematics, physics, engineering, and navigation. It helps in solving problems involving right triangles, calculating slopes, and determining angles of elevation or depression.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in any consistent units. 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, as the function is periodic with period π.

Q2: What happens when the adjacent side is zero?
A: The tangent becomes undefined (approaches infinity) as the angle approaches 90 degrees.

Q3: Can tangent values be negative?
A: Yes, in quadrants II and IV where either opposite or adjacent (but not both) are negative.

Q4: How is tangent related to other trig functions?
A: tan(θ) = sin(θ)/cos(θ). It's also the reciprocal of the cotangent function.

Q5: What are practical applications of tangent?
A: Used in calculating heights of buildings, angles in construction, navigation, and in many physics formulas involving angles.