SIN Excel function is an inbuilt trigonometric function in excel which is used to calculate the sine value of given number or in terms of trigonometry the sine value of a given angle, here the angle is a number in excel and this function takes only a single argument which is the input number provided.

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

## SIN Function in Excel

SIN function in Excel computes the Sine of an angle that we specify. SIN in Excel function is categorized as a Math/Trigonometry function in Excel. SIN in excel always returns a numeric value.

In mathematics and trigonometry, the SINE is a trigonometric function of an angle, which in a right-angled triangle is equal to the length of the opposite side (the right-angled side), divided by the length of the hypotenuse, and represented as:

Sin Θ = opposite side/ hypotenuse

Sin Θ = a/h

### SIN Formula in Excel

Below is the SIN Formula in Excel.

Where number is an argument passed to the SIN Formula in radians.

If we directly pass the angle to SIN in excel function, it will not recognize it as a valid argument. For example, if we pass 30° as the argument to this SIN in Excel function it will not recognize it as a valid argument. The Excel will display an error message.

Hence, the argument that we need to pass must be in **radians. **

To convert an angle into a radian, there are two methods

- Use the inbuilt Excel RADIANS function. The RADIANS function converts the degrees to a radian value.

For example, to convert 30° to radian we will use this function, it takes the degree as a number, it will 30° as 30.

=**RADIANS(30)** will give the radian 0.52

- In the second case we can use the mathematical formula for conversion of a degree to radian. The Formula is

**Radian = degrees * (π/180) (π =3.14)**

In excel also have a function that returns the value of Pi, accurate to 15 digits, and the function is **PI()**

Therefore, for degree to radian conversion, we would use the formula

Radian = degrees * (PI()/180)

### How to Use SIN Function in Excel?

SIN Function in Excel is very simple and easy to use. Let understand the working of SIN in excel by some examples.

### SIN in Excel Example #1

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

Calculating Sine Value using SIN Function in Excel and PI Function

Sine function in Excel has many real-life applications; it is widely used in architectures to calculate the heights and lengths of geometric figures. It is also used in GPS, optics, calculating trajectories, to find the shortest route based on latitude and longitude geographical location, radio broadcasting, etc. Even an electromagnetic wave is plotted as graph of sine and cosine function.

Suppose we have three right-angled triangles, given with their angles and length of one side and we need to calculate the length of the other two sides.

The sum of all the angles on a triangle is equal to 180°, therefore, we can easily calculate the third angle.

We know, Sin Θ = opposite/hypotenuse

So, opposite side length will be **Sin Θ * hypotenuse**

In Excel, the length of Opposite side (perpendicular side), will be calculated by the SIN formula

**=SIN(RADIANS(C2))*E2**

Applying the above-given SIN formula for three triangles we can get the length of perpendiculars of triangles

For the third side (adjacent side), we have two methods – by using Pythagoras theorem or by again using the SIN in Excel function from other angles.

According to Pythagoras theorem, the sum of squares of two side of the right-angled triangle is equivalent to the square of the hypotenuse.

**Hypotenuse ^{2 }= Opposite^{2 }+ Adjacent^{2}**

Adjacent = (Hypotenuse^{2} – Opposite^{2})^{1/2}

In excel, we will write it as,

**=POWER((POWER(Hypotenuse,2)-POWER(Opposite,2)),1/2)**

Applying this formula, we compute the length of the adjacent side

**=POWER((POWER(E2,2)-POWER(F2,2)),1/2)**

Using the second method, we can use the SINE of 3^{rd} angle to calculate the value of the adjacent side

If we rotate the triangles to 90° left, the opposite side is swapped with the adjacent side and the SIN of angle between hypotenuse and adjacent will help to calculate the value of the third side.

**=SIN(RADIANS(D2))*E2**

### SIN in Excel Example #2

There is a tall building of unknown height and Sun ray at a point of time makes an angle at point A of 75°, thus making a shadow of the building of length 70 meters. We need to find the height of the tower

Height of building will be calculated using the SIN in excel function

SIN 75° = Height of Building/ Length of Shadow at point A

Therefore, the height of building = **SIN 75° * Length of Shadow at point A**

Hence, Height of building will be

**=SIN(RADIANS(B3))*B2**

**Height of Building is 67.61 meters**

### SIN in Excel Example #3

We have a land in a form of a triangle, for which the two angles are given as 30° and 70° and we only know the length of one side of the triangle which is 40 meter. We need to find the length of other three sides and the perimeter of the triangle.

For a triangle, when one side and all angles are known we can calculate the other sides by SINE Rule

Sine Rule in Trigonometry gives a relation of sin angles and sides of a triangle by a SIN formula

**a/sin α = b/sin ß = c/sin δ **

In this case,

α = 30°, ß = 70° and δ = 180°-(30°+70°) = 80° and one side of triangle b = 40 meters

To find the other sides of the triangle we will use the SINE Rule

a = Sin α * (b/sin ß)

Therefore,

**a =SIN(RADIANS(30))*(B5/SIN(RADIANS(70)))**

Length of side a = 21.28 meters

Similarly, third side c will be

c = Sin δ * (b/sin ß)

Therefore,

**c =SIN(RADIANS(80))*(B5/SIN(RADIANS(70)))**

The three sides of the triangle are of length 21.28, 40, 41.92 meters.

The Perimeter of the triangle is sum of all the sides.

Therefore, the perimeter will be **=SUM(B5:B7)**

### SIN Excel Function Video

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