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 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 : where 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:
(*) 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
What is the sin of 2 theta?
The sine of 2 theta (
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.
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).