 # Lesson 7: Trigonometric Functions

In this lesson, we shall learn how to work with trigonometric functions. The three basic trigonometric functions are sin, cos and tan which stand for sine, cosine and tangent. We also deal with the inverse of tangent, Atn.

## 7.1 The sin function

The sin function returns the sine value of an angle. We need to convert the angle to radian as Excel VBA cannot deal with angle in degree. The conversion is based on the following equation:

The issue is how to get the exact value of p? We can use p=3.14159 but it will not be accurate. To get exact value of π, we use the arc tangent function, i.e. is Atn. Using the equation tan(π/4)=1, so Atn(1)=π/4, therefore, π=4Atn(1)

The syntax of the Sine function in Excel VBA is

`sin(Angle in radian)`

### Example 7.2

In this example, we use pi to represent π and assign the value of π using the formula pi = 4*.Atn(1). We use the function Round the value of sine to four decimal places.

```Private Sub CommandButton1_Click()

Dim pi As Single
pi = 4*.Atn(1)
MsgBox("Sin 90 is" & Round(sin(pi/2), 4))

End Sub
```

Running the program produces the message as shown in Figure 7.1

## 7.2 The cos function

The cos function returns the cosine value of an angle

The syntax of the Cos function in Excel VBA is

`cos(Angle in radian)`

### Example 7.2

```Private Sub CommandButton1_Click()

Dim pi As Single
pi = 4*.Atn(1)
MsgBox("Cos 60 is" & Round(Cos(pi/3), 4))

End Sub
```

Running the program produces the message as shown in Figure 7.2

## 7.3 The tan function

The tan function returns the tangent value of an angle

The syntax of the tan function in Excel VBA is

`tan(Angle in radian)`

### Example 7.2

```Private Sub CommandButton1_Click()

Dim pi As Single
pi = 4*.Atn(1)
MsgBox("Tan 45 is" & Round(tan(pi/3), 4))

End Sub
```

Running the program produces the message as shown in Figure 7.3