Sine Calculator

How to Calculate Sine

The sine function, denoted as sin(x), is a fundamental trigonometric function that relates the angles of a right triangle to the ratios of the lengths of its sides. It is widely used in various fields of mathematics, physics, and engineering.

Formula

The sine of an angle θ in a right-angled triangle is defined as:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]

Where:

• sin(θ) is the sine of the angle θ
• opposite is the length of the side opposite to the angle θ
• hypotenuse is the length of the longest side of the right triangle
• θ is the angle in radians

Calculation Steps

1. Ensure the angle is in radians. If it's in degrees, convert it to radians by multiplying by π/180°.
2. Use a calculator or trigonometric tables to find the sine value of the angle.
3. The result will be a value between -1 and 1, inclusive.

Example

Let's calculate sin(30°):

1. Convert 30° to radians: 30° × (π/180°) = π/6 radians
2. Calculate sin(π/6) ≈ 0.5

Therefore, sin(30°) = 0.5

Visual Representation

This diagram illustrates sin(30°). The blue line represents the angle of 30°, and the red line shows the sine value of 0.5 on the y-axis.