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

Anglesin 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

Frequently Asked Questions

What is the sine function?

Sine is a trigonometric function that gives the ratio of the opposite side to the hypotenuse in a right triangle, or the y-coordinate on the unit circle.

What is the range of sine?

The sine function outputs values between -1 and 1. sin(90°) = 1 and sin(270°) = -1.

What is the period of sine?

Sine has a period of 360° (2pi radians). The function repeats every full rotation.

Learn More

Guide

Trigonometry Basics - Complete Guide

Learn the fundamentals of trigonometry including sine, cosine, tangent, the unit circle, identities, and the laws of sines and cosines with practical examples.

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