Calculate the sine of an angle using degrees or radians. This calculator supports both units and shows the result with 6 decimal precision.
The Sine Calculator is a powerful online tool designed to calculate the sine of any angle in degrees or radians. Whether you're a student learning trigonometry, an engineer working on wave analysis, or a developer solving for geometry, this calculator offers precise, instant results with ease. Forget memorizing sine values or consulting trigonometric tables—just enter the angle and get the sine value immediately.
In trigonometry, sine (sin) is a fundamental function that relates the angle of a right triangle to the ratio of the opposite side to the hypotenuse. For any angle θ:
sin(θ) = Opposite / Hypotenuse
This ratio is consistent regardless of the triangle's size, making it an essential tool in geometry, physics, and engineering.
It's that simple. You can toggle between Degrees and Radians based on your input source or mathematical requirement.
Here are a few commonly used sine values that our calculator can return instantly:
| Angle (Degrees) | Angle (Radians) | sin(θ) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.5 |
| 45° | π/4 | 0.7071 |
| 60° | π/3 | 0.8660 |
| 90° | π/2 | 1 |
| 180° | π | 0 |
The sine function is periodic and oscillates between -1 and 1. Its graph is a smooth wave (sinusoid) that repeats every 360° (or 2π radians).
Sine functions are used in various fields beyond basic trigonometry:
Given a right triangle with angle θ, opposite side a, and hypotenuse c:
sin(θ) = a / c
For example, if the opposite side is 4 and the hypotenuse is 5, then sin(θ) = 4 / 5 = 0.8
In calculus and scientific calculations, angles are usually in radians, while in school math and geometry, degrees are more common. This calculator supports both:
The sine values are calculated using the JavaScript Math library with precision up to 10 decimal places. For most practical cases, 4-6 digits of accuracy are sufficient, but you can copy the full value if needed for scientific or engineering reports.
Q1: What is sin(120°)?
Answer: sin(120°) = sin(60°) = 0.8660
Q2: Convert sin(π/3) from radians.
Answer: sin(π/3) = 0.8660
Q3: If the hypotenuse is 10 and the opposite side is 6, what is sin(θ)?
Answer: sin(θ) = 6 / 10 = 0.6
Free online Sine Calculator – instantly find the sine of any angle in degrees or radians. Accurate results with clean UI, ideal for students and professionals.
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The Sine Calculator is more than just a quick computation tool — it’s a powerful educational resource that simplifies the understanding of one of the most fundamental trigonometric functions. Whether you're in school, college, or the professional world, this calculator will save you time and improve accuracy across all types of mathematical applications. Try it now!
One of the most powerful ways to understand sine is through the unit circle. The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. In this model:
sin(θ) equals the y-coordinate of the point on the unit circle at angle θ from the positive x-axis.
This visualization helps students grasp sine’s periodic and wave-like behavior.
The graph of the sine function is called a sine wave or sinusoid. It’s a smooth, continuous curve that:
Sine waves are fundamental in understanding AC currents, sound waves, radio signals, and harmonic motion.
Sine waves are the simplest form of sound. They represent a single frequency and are used in:
This makes sine calculations crucial for musicians, audio engineers, and acoustic researchers.
Sine functions are used in designing curves and wave-like structures. Architects and designers use trigonometric functions like sine to model:
Sine is key to describing circular and rotational motion. In uniform circular motion, an object’s vertical position is modeled by:
y(t) = r × sin(θ)
Where:
This is used in physics, mechanics, astronomy, and engineering simulations.
To find the angle from a known sine value, we use the inverse sine function:
θ = sin⁻¹(x) or θ = arcsin(x)
Example: If sin(θ) = 0.5, then θ = 30° (or π/6 radians). This function is also built into many calculators and math software for reverse computations.
Programming languages like Python, JavaScript, and C++ have built-in sine functions. Example in JavaScript:
let result = Math.sin(angleInRadians);Use cases include simulations, animation paths, game development, and robotics.
Alternating current (AC) follows a sine wave pattern. Calculations involving voltage, frequency, and impedance often involve sine:
V(t) = V₀ × sin(ωt + φ)
Where V₀ is peak voltage, ω is angular frequency, and φ is phase shift.
From earthquakes to medical imaging, sine functions model real-world signals:
We are working on translating this calculator and its explanations into multiple languages to support global learners, including:
Whether you’re decoding sound waves, solving right triangles, or building rotating animations, the Sine Calculator simplifies complex math into a click. Explore the world of oscillations, harmony, and periodic motion with confidence — powered by Easy Converters.