**Excel SIN Function** **(Table of Contents)**

## SIN Function in Excel

Being able to calculate does not encompass the entirety of mathematics. It’s a subsection of it, albeit vital in its application. In years gone by it was the limiting factor, except for the much renowned and supremely talented ‘human calculators’, such as Shakuntala Devi. But computers now allow you to make the whole of mathematics more intellectual. The concepts and theorems of mathematics are more prominent now than ever before.

Excel is very adept at handling a plethora of mathematical models, is armed with a vast collection of mathematical and logical functions to support various operations. It provides a whole suite of trigonometric functions to aid us when we foray into the world of trigonometry.

So, to solve the trigonometric function **Sine**, it provides the **SIN function**. It is a basic trigonometric function but comes in handy particularly if you are working in manufacturing, Navigation or Communication Industries. But it is important to note Excel uses radians, not degrees to calculate any trigonometric expression. There are two ways of going about this:

- Recall that π = 180°. So, if the angle is in degrees, multiply it by π /180° to convert it to radians. In Excel, this conversion can be written PI( )/180. For example, to convert 60° to radians, the Excel expression would be 60*PI( )/180 which equals 1.0472 radians.
- Excel is also equipped with a very useful tool commonly referred to as RADIANS. It accepts an angle as an argument, in which the angle refers to the degrees that have to be transformed into radians. Take the instance where the expression that is utilized to transform 210° into radians is “RADIANS(210)”, and it evaluates to 66519 radians.

Conversely, the DEGREES utility is equally important. This function can be used to do the exact opposite of the RADIANS function, by converting radians to degrees. As an example, DEGREES(PI( )/2 ) evaluates 90.

**How to use SIN function in Excel?**

Let’s understand how to use SIN Function in Excel by using some examples and real-life illustrations of SIN Function in Excel.

### SIN Function in Excel – Example #1

**Calculating Sine Value using SIN Function in Excel**

To find the sine of a particular number, we have to first write **=SIN( )** in a particular cell.

As you can see from the above screenshot, the SIN function in Excel expects a number as an input. This number usually represents a value in radians.

So in this case, we will write “=SIN(1.0472)”, where 1.0472 is the radians equivalent of 60 degrees.

Once we do this, we will get the SIN value of 60 degrees.

### SIN Function in Excel – Example #2

**Calculating Sine Value using SIN and RADIAN Function in Excel**

Now let us see how we can use SIN in a more productive way, in case when we don’t know the exact radian value for a degree.

We will use the RADIANS() to find out the radian value, which we will pass as an argument to the SIN function.

So, we start off with the earlier version of the SIN( ):

Next, we will pass **RADIANS(60)** as an argument to the SIN function, where **60** is the value in degrees.

As we can see from the example above, RADIANS() accepts a value in degrees. So, we shall pass 60 as the value to RADIANS().

Then Press **Enter.** This yields the following result.

So, we see that the result is the same as the first example.

### SIN Function in Excel – Example #3

**Calculating Sine Value using SIN and PI ****Function in Excel**

There is yet another way to convert a degree value to radians for our use in the SIN function. We remember from our time in school that π = 180°. So, if the angle is in degrees, multiply it by π/180° to convert it to radians. In Excel, this conversion can be written PI( )/180. For example, to convert 60° to radians, the Excel expression would be 60*PI( )/180 which equals 1.0472 radians.

Let us see how this works:

We begin by writing the SIN function in the same way as above.

Next, we will directly pass **60°** as the argument to the SIN function. But this wouldn’t give us the corresponding value of 60 degrees in radians. Hence we will multiply 60 by **PI()/180.**

This will give us the following result:

As we can see, this is the same as the above examples.

### SIN Function in Excel – Example #4

Now, let’s look at another example showing the results of the SIN function for various values.

Explanation of the results shown in the above table:

**Case 1 and 2 :**

3.14 is the value of Pi and we can use both methods to get a value of 0. This basically means **SIN of Pi radians** is **0**.

**Case 3 and 4 :**

Radians and Pi/180 have equal value in mathematics and hence SIN function gives the same value. Both examples imply SIN of 30 degrees which gives a value of 0.5.

**Case 5 and 6 :**

SIN 45 = 0.85 is SIN of 45 radians which means by default excel takes all the angles in radians and not degree. To convert it into degree we can use radian function and get SIN of 45 degrees as shown in the last row. i.e. SIN(RADIANS(45)) = 0.707 or 0.71

### SIN Function in Excel – Example #5

Say, for example, we want to know the height of the tree in the figure shown above. We know that if we stand 76 m from the top of the tree (x = 76 m) the line of sight to the top of the tree is 32° with respect to the horizon (θ = 32°). We know that:

Hence in order to solve for the height of the tree h, we find **h= x SIN θ.**

SIN function has only one argument which is a number. A number is required to calculate SIN of it. Hence it is vital to convert degrees to a number in radians before finding the Sine of it.

The SIN function displays the **#VALUE!** error if the reference used as the function’s argument points to a cell containing text data. In the example shown below, the cell reference of the third row used points to the text label in Angle** (Degrees)**. Since the SIN functions only support a number as an argument, SIN will evaluate to an error, in this case, **#VALUE!**. If the cell points to an empty cell, the function returns a value of zero as shown in the example below. Excel’s trigonometric functions interpret blank cells as zero, and the sine of zero radians is equal to zero.

### SIN Function in Excel – Example #6

Now, suppose we want to find out the launch angle of a water ski ramp as in the figure above. We know that A = 3.5 m, B = 10.2 m and b = 45.0°. Now in order to find **a**, we can use the Law of sines. In this scenario, it can be written as:

We can re-organize this equation as:

Using the arcsine or inverse sine, we can find out the angle **α**. Applying the equation shown below.

### Example #7

In our final trigonometric example, we will use Excel to examine the trigonometric identity:

**sin²θ + cos²θ = 1**

Note that in the screenshot below, this identity holds true when θ is given in both radians and degrees.

Note the unit description for the angle θ is placed in different cells than the numbers. If we place the numbers and the units in the same cell, Excel will not be able to differentiate the number from the text and therefore we will not be able to reference the cells for use in an equation and it would result in **#VALUE!** error.

**Things to remember**

- Keep in mind that the SIN function in excel works with Radian by default.
- Convert the number as required in Radian or Degree using either RADIANS function or DEGREES function.
- You can use PI() function to get exact results of SIN function while working with π.

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