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Sine Calculator

Sine calculator computes sin(theta) from any angle in degrees. sin(30) = 0.5, sin(45) = 0.7071, sin(90) = 1. Instantly convert degree input to the exact sine value for trigonometry, physics, and engineering problems.

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Formula

#
Core Formula
sin(θ)\sin(\theta)

How it works: Converts degrees to radians (multiply by pi/180), then evaluates the sine function.

Worked Example

Find sin(30 degrees).
1Step 1: Convert to radians: 30 x (pi/180) = pi/6 = 0.5236 radians.
2Step 2: sin(pi/6) = 0.5. Common reference values: sin(0) = 0, sin(30) = 0.5, sin(45) = 0.7071, sin(60) = 0.8660, sin(90) = 1. For a right triangle with hypotenuse 10 and angle 30 degrees, the opposite side = 10 x sin(30) = 10 x 0.5 = 5.

How the Sine Function Works

Sine is one of the three primary trigonometric functions. In a right triangle, sin(theta) equals the length of the opposite side divided by the hypotenuse.

  • sin(theta) = opposite / hypotenuse in a right triangle
  • Key values: sin(0) = 0, sin(30) = 0.5, sin(45) = 0.7071, sin(60) = 0.8660, sin(90) = 1
  • Sine is positive in quadrants I (0-90) and II (90-180), negative in quadrants III (180-270) and IV (270-360)
  • The sine function has a period of 360 degrees, meaning sin(theta) = sin(theta + 360)

This calculator accepts degrees and handles the conversion to radians internally. For inverse sine (finding the angle from a ratio), use an arcsin calculator.

You can also calculate changes using our Cosine Calculator, Tangent Calculator or Arctan Calculator.

Frequently Asked Questions

What is sin(45) degrees?

sin(45 degrees) = sqrt(2)/2, which is approximately 0.7071. This is one of the most commonly used trig values and appears frequently in physics, engineering, and geometry problems involving 45-45-90 triangles.

How do I convert degrees to radians for sine?

Multiply the degree value by pi/180. For example, 30 degrees = 30 x pi/180 = pi/6 radians. This calculator handles the conversion automatically, so you just enter degrees.

What are the common sine values I should memorize?

The five essential values: sin(0) = 0, sin(30) = 0.5, sin(45) = 0.7071, sin(60) = 0.8660, sin(90) = 1. These come from the special 30-60-90 and 45-45-90 reference triangles and appear constantly in math and science.

When is the sine of an angle negative?

Sine is negative when the angle is in quadrant III (180 to 270 degrees) or quadrant IV (270 to 360 degrees). For example, sin(210) = -0.5 and sin(330) = -0.5. Sine is positive in quadrants I (0-90) and II (90-180).

Can I use negative angles or angles greater than 360?

Yes. sin(-30) = -0.5, and sin(390) = sin(30) = 0.5 because sine has a period of 360 degrees. The calculator handles any real number input and returns the correct sine value.

How do I add this Sine Calculator to my site?

Absolutely. Use the "Embed" option above to tailor the dimensions, color scheme, and styling to match your site. Copy the generated iframe snippet and drop it into your HTML, WordPress editor, or any CMS. There is no cost and no account required. See calculory.com/services/embed-calculators for a step-by-step walkthrough.

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