Sine Calculator (Degrees and Radians)


Answer:


Graph of sine (radians and degrees)

With this calculator, you can get the sine of any entered angle. When you enter an angle, the calculator will display the sine of that angle immediately. It is possible to use both degrees and radians.

Below you will find additional information regarding the use of the calculator. In addition, you will be able to learn more about the sine of an angle in general. You will find the definition of sine, its graph, and the sine values of important angles.

How to use the sine calculator?

Step 1: Click the blue button to select the type of angle you are going to enter. You have the option to use degrees, radians, or π radians.

Step 2: Enter the angle in the “Angle” input box. It is possible to use both positive and negative numbers.

Step 3: The sine of the angle will be displayed immediately on the right panel.

Difference between degrees, radians, and π radians on the calculator

A complete circle has a total of 360°, which is equivalent to 2π radians. Therefore, we can deduce that 180° is equivalent to π radians.

Now, remembering that π has a value of approximately 3.1415…, we can deduce that π radians is approximately 3.1415 radians. So, depending on the angle we want to enter, we must select between the three available options.

For example, if we want to find the sine of the angle 60°, we can do any of the three equivalent options:

  • We can select “degrees” and enter 60.
  • We can select “π radians” and enter 0.3333 (180° equals π radians, so 60° equals 1/3 π radians).
  • We can select “radians” and enter 1.0472 (0.3333π radians equals 1.0472 radians).

What is the sine of an angle?

Sine is one of the fundamental trigonometric functions, along with cosine and tangent. We can define the sine of an angle using a right triangle. So, the sine is equal to the length of the side opposite the angle divided by the length of the hypotenuse of the triangle.

For example, using the following right triangle, we can define the sine of angle A as the length of side a (side opposite A) divided by the length of side c (hypotenuse and opposite the 90° angle).

In addition, we can define the sine of angle B as the length of side b (side opposite B) divided by the length of side c (hypotenuse).

diagram-of-a-right-triangle-with-sides

If you want to learn more about the sine of an angle, visit our article Sine of an Angle – Formulas and Examples.

Graph of the sine of an angle

The sine of an angle can be extended to use angles that are outside of a right triangle. This means that the sine function can take both positive and negative angles greater than 180°.

The sine function is periodic, that is, this function repeats itself after a constant interval. In the case of the sine function, its period is equal to 360° or 2π.

Graph of sine (radians and degrees)

Domain of the sine of an angle

From the graph of sine, we can deduce that any value can be used as input. That is, we can use any angle, both positive and negative, no matter how big it is.

Therefore, the domain of the sine function is equal to all real numbers.

Range of the sine of an angle

From the sine graph, we can conclude that the output values range from -1 to 1. The sine function cannot output values that are greater than 1, so its range is equal to -1 ≤ cos(α) ≤ 1.

Sine of common angles table

DegreesRadiansSine
-90°-π/2-1
-60°-π/3-√3/2
-45°-π/4-√2/2
-30°-π/6-1/2
00
30°π/61/2
45°π/4√2/2
60°π/3√3/2
90°π/21

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