Sine Calculator

How to Calculate or Solve Sine (sin)

The sine of an angle is a fundamental concept in trigonometry. It can be calculated using a right-angled triangle or by evaluating a known angle in degrees or radians.

1. Sine in a Right-Angled Triangle

In a right triangle, the sine of an angle is the ratio of the length of the side opposite to the angle divided by the hypotenuse.

Steps:

1. Identify the angle θ.
2. Measure the opposite side to the angle.
3. Measure the hypotenuse (longest side).
4. Divide the opposite side by the hypotenuse.

Example:

If the opposite side is 3 and the hypotenuse is 5:

2. Sine of Known Angles

Sine values for common angles are well-known and often used in geometry and trigonometry.

• sin(0°) = 0
• sin(30°) = 1/2 = 0.5
• sin(45°) = √2/2 ≈ 0.707
• sin(60°) = √3/2 ≈ 0.866
• sin(90°) = 1

3. Degrees and Radians

Angles can be expressed in degrees or radians. The formula to convert degrees to radians is:

Example: 60° = 60 × (π / 180) = π/3 radians

Key Points:

• Sine values range from -1 to 1.
• sin(0) = 0, sin(90°) = 1, sin(180°) = 0
• Sine is positive in the 1st and 2nd quadrants of the unit circle.