# Sin Theta Calculator

Created by Luciano Miño
Reviewed by Luis Hoyos
Last updated: Jan 24, 2023

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

## 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 . 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:

 $\sin(-x)$ $= -\sin(x)$ $\sin^2(x)$ $= 1 - \cos^2(x)$ $\sin(2x)$ $= 2\cdot \sin(x) \cdot \cos(x)$ $\sin(\frac{x}{2})$ $= \pm \sqrt{\frac{1 -\cos(x)}{2}}$ $\sin(x+y)$ $= \sin(x)\cos(y) + \cos(x)\sin(y)$ $\sin(x-y)$ $= \sin(x)\cos(y) - \cos(x)\sin(y)$ $\frac{d}{dx}\sin(x)$ $= \cos(x)$ (*)

🙋 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:

## 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:

1. Write down the sine half-angle equation: sin(θ/2) = ±√[(1-cos(θ))/2].
2. Replace theta θ within the equation and solve the square root.
3. 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.

### 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).

Luciano Miño
Angle
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