1. What is the Sine Function in Trigonometry?

Definition: The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

Purpose: It's fundamental in trigonometry for solving right triangle problems and modeling periodic phenomena.

2. How Does the Sine Formula Work?

The calculator uses the formula:

Where:

• \( \theta \) — Angle in degrees (between 0° and 90°)
• opposite — Side opposite to the angle θ (in meters)
• hypotenuse — Longest side of the right triangle (in meters)

Explanation: The calculator can find any one missing value when the other two are known.

3. Importance of Sine Function

Details: The sine function is essential in physics, engineering, architecture, and many fields involving wave motion, circular motion, and periodic phenomena.

4. Using the Calculator

Tips: Enter any two values (opposite side, hypotenuse, or angle) to calculate the third missing value. Angle must be between 0° and 90°.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of valid angles for this calculator?
A: The calculator works for angles between 0° and 90° (right triangle angles).

Q2: What units should I use for the sides?
A: The calculator uses meters, but any consistent unit can be used as long as both sides use the same unit.

Q3: Can I use this for non-right triangles?
A: No, this specific formula only applies to right triangles. For other triangles, use the Law of Sines.

Q4: How precise are the calculations?
A: Results are displayed with 2 decimal places for angles and 3 decimal places for lengths.

Q5: What if I get an error message?
A: Ensure your values make mathematical sense (e.g., opposite side cannot be longer than hypotenuse).