# Sin Theta Calculator

The sin theta calculator can aid you in your math problems and **obtain the sine value of any angle**.

We've paired this calculator with a few paragraphs covering:

- What is the definition of
**sin**(sine definition); - What sin of 0 is;
- Properties of sine; and
**More about this particular trigonometric function**📐

*Keep reading to learn more!*

## What is the definition of sin/sine?

Before we start with the sine function definition, we need to introduce the **unit circle**. This circle is centered at the origin, and its radius equals one.

If we draw a line from the origin to any point on this unit circle, an angle theta $\theta$ will be formed between this radius and the **horizontal axis**.

The **sine**, or **sin**, is the **y-axis** coordinate of this radius as the angle changes describing any point on the unit circle.

Like **cosine**, sine is a periodic function with a period of **2π**. This means that for any argument $\theta$: $\sin(\theta + 2k\pi) = \sin(\theta)$ where $k$ is any integer.

💡 *Test it out!* Input any angle in our sin theta calculator and write down the sine result. Now try again with the same angle, but **add 2*π** (or 360°, if you're using degrees) to it and see if the results match.

## Properties of sine

Here's a list of some of the sine properties and trigonometric identities involving the sine function:

$\sin(-x)$ | $= -\sin(x)$ |

$\sin^2(x)$ | $= 1 - \cos^2(x)$ |

$\sin(2x)$ | $= 2\cdot \sin(x) \cdot \cos(x)$ |

$\sin(\frac{x}{2})$ | $= \pm \sqrt{\frac{1 -\cos(x)}{2}}$ |

$\sin(x+y)$ | $= \sin(x)\cos(y) + \cos(x)\sin(y)$ |

$\sin(x-y)$ | $= \sin(x)\cos(y) - \cos(x)\sin(y)$ |

$\frac{d}{dx}\sin(x)$ | $= \cos(x)$ (*) |

(*) *Only when using radians.*

🙋 You can input the sine argument in either **degrees**, **radians**, or **π radians** with our sin theta calculator!

## Other sine calculators

Feel free to check our other tools related to the sin theta calculator:

- Sine calculator;
- Sine function calculator; and
- Sin degrees calculator.

## FAQ

### What is the sin of 2 theta?

The sine of 2 theta (`2θ`

) equals `2 sin(θ)cos(θ)`

. According to one of the sine properties: `sin(2x) = 2sin(x)cos(x)`

. So, if you know the values for the sine and cosine of theta, you can easily find the sine of 2 theta.

### How do I find the sin of theta/2?

To find the sin of theta/2:

- Write down the sine half-angle equation:
`sin(θ/2) = ±√[(1-cos(θ))/2]`

. - Replace theta θ within the equation and solve the square root.
- To choose the sign, follow this rule:
- The result is
**positive (+)**if the half angle lies in the**I**or the**II**quadrant; or **Negative (-)**if it lies on the**III**or**IV**quadrant.

- The result is

### What is the sin of 0?

**0**. The value for the sine function at 0 is 0. The **y-axis** component of the radius in the unit circle is **0** when the radius lies on the horizontal axis (which corresponds to angle zero).