Sine Calculator
Use this sine calculator to easily and quickly calculate the sine of an angle given in degrees or radians .
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About Sine
Here on this page we understand about sine
Sine – Mastering the Wobble Factor in Trigonometry
Imagine a Ferris wheel. As a cabin goes round and round, its height (up and down) constantly changes. That up-and-down motion is exactly what the sine function describes in trigonometry, but instead of a Ferris wheel, we use angles.
Table of Contents
The Sine Function (sin(x)) - It's All About Ratios
The sine of an angle (written as sin(x), where x is the angle) tells you the ratio between the opposite side (the side facing the angle) and the hypotenuse (the longest side) of a right triangle. It’s like a special recipe for figuring out how “high up” the opposite side is compared to the whole triangle.
Trigonometry's Family
Sine has two best buddies in trigonometry -cosine (cos(x)) and tangent (tan(x)). Cosine deals with the ratio opposite to the adjacent side (the side next to the angle), and tangent is the opposite over the adjacent. They all work together to unlock the mysteries of triangles and angles.
formula for calculating sine
following formula -
In a unit circle, where the radius is 1, the sine of an angle θ is the y-coordinate of the point where the terminal side of the angle intersects the unit circle.
So, in mathematical terms:
sin(θ) = opposite / hypotenus
θ (theta) is the angle you’re interested in (usually the one opposite the side lengths you know).
opposite is the side of the triangle directly opposite the angle (theta).
hypotenuse is the longest side of the right triangle, always opposite the right angle.
Note – Make sure you know if your angle is measured in degrees or radians before using the sine function on your calculator!
common sine values:
| x (°) | x (rad.) | sine(x) |
|---|---|---|
| -90° | -π/2 | -1 |
| -60° | -π/3 | -√3/2 |
| -45° | -π/4 | -√2/2 |
| -30° | -π/6 | -1/2 |
| 0 | 0° | 0 |
| 30° | π/6 | 0.50 |
| 45° | π/4 | 0.707107 |
| 60° | π/3 | 0.866025 |
| 90° | π/2 | 1 |
| 120° | 2π/3 | 0.866025 |
| 135° | 3π/4 | 0.707107 |
| 150° | 5π/6 | 0.50 |
| 180° | π | 0 |