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.
definition of sine function

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.
sine functions

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 functions 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.
sine function table

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

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°).


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°).


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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