Domain of Sine

The domain of trigonometric function sine is the set of angles for which the sine function is defined. The domain of sine is input for this function and the all values of this trigonometric ratio are determined by putting domain’s values in angle’s place. In few steps you are going to understand this concept clearly.

As we already know by considering a right angle triangle, the ratio of opposite side and the hypotenuse is known trigonometric ratio Sine and it can be expressed in mathematical form by assuming the angle of a right angle triangle is Theta.

Sin θ

=

Opposite Side Hypotenuse

The domain of this function actually represents the angle (theta) in this case. As the opposite side value changes i.e either increased or decreased, the angle will be changed. In other words, If the length of the opposite side is increased, the angle of the triangle is also increased.

Whatever values you put in sine function’s angle area, it gives corresponding value. By collecting all those values for different angles, we plot a sine graph by considering angles in horizontal axis and its values for the respective angles in vertical axis as shown in the graphical presentation. In this graphical presentation, you have to understand, the domain of the sine represents set of all values on horizontal axis.

Domain of sine function includes rational numbers, irrational numbers, positive numbers, negative numbers, zero and integers but does not work for undermined values such as imaginary values, complex numbers and infinity. The pros and cons of this function exactly meet the property of real numbers group. Therefore, the domain of Sine function is Real Number Group. In other words, for the set of all values of real numbers group, sine function is defined. It simply represents with English alphabet R symbol. In other words, the domain of a sine function is R.