Sine Calculator Formula

Understand the math behind the sine calculator. Each variable explained with a worked example.

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Formulas Used

Sine Val

sine_val = sin(angle_deg * pi / 180)

Cosine Val

cosine_val = cos(angle_deg * pi / 180)

Tangent Val

tangent_val = tan(angle_deg * pi / 180)

Radians

radians = angle_deg * pi / 180

Variables

VariableDescriptionDefault
angle_degAngle (degrees)(deg)30

How It Works

Sine Function

Definition

In a right triangle, sin(angle) = opposite / hypotenuse.

On the unit circle, sin(angle) is the y-coordinate of the point at that angle.

Key Values

| Angle | sin | |-------|-----| | 0° | 0 | | 30° | 0.5 | | 45° | √2/2 ≈ 0.7071 | | 60° | √3/2 ≈ 0.8660 | | 90° | 1 |

Worked Example

Calculate sin(30°).

angle_deg = 30
  1. 0130° in radians = 30 × pi/180 = pi/6 ≈ 0.5236
  2. 02sin(30°) = 0.5
  3. 03cos(30°) = √3/2 ≈ 0.8660
  4. 04tan(30°) = 1/√3 ≈ 0.5774

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