1. What are Trigonometric Ratios?

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The primary ratios are sine (sin), cosine (cos), and tangent (tan), each representing a specific relationship between the sides of the triangle.

2. How Does the Calculator Work?

The calculator uses the fundamental trigonometric ratios:

Where:

• \( θ \) — Angle between adjacent side and hypotenuse
• Opposite — Side opposite to angle θ
• Adjacent — Side adjacent to angle θ
• Hypotenuse — Longest side of the right triangle

Explanation: These ratios remain constant for a given angle regardless of the triangle's size, making them fundamental in trigonometry.

3. Importance of Exact Values

Details: Exact values provide precise calculations for trigonometric functions without rounding errors, essential in fields like engineering, physics, and navigation.

4. Using the Calculator

Tips: Enter all three side lengths in the same units. Values must be positive numbers that satisfy the Pythagorean theorem (a² + b² = c²).

5. Frequently Asked Questions (FAQ)

Q1: What if my triangle isn't right-angled?
A: These formulas only work for right triangles. For other triangles, you would need to use the Law of Sines or Cosines.

Q2: Can I use this for any angle measurement?
A: These ratios are defined for angles between 0° and 90° in right triangles. For other angles, you'd need the unit circle definitions.

Q3: What units should I use?
A: Any consistent length units (cm, m, inches, etc.) can be used as long as all sides are in the same units.

Q4: Why are exact fractions important?
A: Exact fractions maintain precision in calculations, especially important in mathematical proofs and precise engineering applications.

Q5: How accurate are the results?
A: The results are mathematically exact when using exact input values, though displayed as decimals for practical use.