# Sin function definition - SOHCAHTOA and circular

For right-angle triangle, the ratio of length of opposite side to length of hypotenuse is called **sin function**. This **definition of sine function** also known as SOHCAHTOA definition.

From above figure we can **define sine function** as,

sin θ = length of opposite side / length of hypotenuse

**Sine functions** also define in terms of circle.

Form above figure **sine function** can be defined as, sin θ = y/r.

**How to decide period of sine function**

**Sin functions** repeat after every 2pi interval. So we can say that **period of sine function** is 2 π. You will shortly observe the same thing in** sine function graph.**

**Sine function graph properties**

** **The process of **graphing sine function**s consists to find values of sine function for some values of angle. The values of sine function for some standard angles are mentioned in below table.

After preparing table, we can plot graph as given below.

After the process of graphing sin function we can conclude some **properties of sine function.**

1)sine function repeats after every 2 π interval, so its period is 2 π and also for sin(2 π+. θ) = sin θ.

2)sine function has value in range of -1 to 1 for all values of angles.

3)sine function exist for all value of angles, so **domain of sine function **is -∞ to +∞.

4)sine is odd function so sin(-θ) = -sin θ.

Now we will see some **sine function examples **to get better idea about its functionality.

**Example 1: **evaluate the value of sin(-750°).

**Solution:**

** **Here, sin(-750°)

= -sin(750°)

= -sin(2*360°+30°)

= -sin(30°)

= -1/2

Now we look little bit harder example.

**Example 2: **evaluate the value of sin(1740°).

**Solution:**

** **Here, sin(1740°)

= sin(4*360°+300°)

= sin((300°)

= sin(360°- 60°)

= sin(-60°)

= -sin(60°)

= -√3 / 2

## Sine Graph Multiple Changes Video Lesson

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