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!

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.

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

(*) Only when using radians.

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

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

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.

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.

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).