The Excel **SIN** function calculates the sine of a given angle. The syntax is as follows:

**SIN**(value)

The value argument of this function is the angle —expressed in *radians*— of which we want to compute for the sine.

**Sine of an Angle**

As a refresher to the concept of sine, consider the right triangle below. For this simple right-angled triangle, the sine of the angle ** θ**, is the ratio of the opposite side,

**, to the hypotenuse,**

*b***.**

*h*

*Figure 1. Find the Sine of an Angle Using SIN Function*

Therefore, for the triangle shown above,

*Figure 2. Find the Sine of an Angle Using SIN Function*

**Converting Angles from Degrees to Radians**

If the angle we are computing the sine for is in degrees, we will need to convert it into radians before using it as an argument to the** SIN** function. Remember that the **SIN** function expects radians. This is where we use another very useful Excel function: **RADIANS**. The syntax of the **RADIANS** function is as follows:

**RADIANS**(degrees)

**Examples of Using the SIN Function**

Consider the following examples:

*Figure 3. Find the Sine of an Angle Using SIN Function*

In the examples shown in Fig.1, note that

- The Excel
**PI**function is used to supply the values**π/6**and**-π/3**respectively in cells**A2**and**A3.**The**PI**function returns the value of pi (π). - In cells
**A4**and**A5**, the**RADIANS**function is used to convert the angles of 30 degrees and -30 degrees to radians before they are supplied as arguments for the**SIN**function.

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