Unit Circle

In the previous post we have discussed about one to one correspondence and In today's session we are going to discuss about Unit Circle. Unit Circle is defined as a circle that is having radius value is equal to 1. Let's us see the steps of making a this circle. Steps of making a circle is given as:

Step 1: To construct a circle it is very essential to have a radius value is equal to one always. If it is not so then it is not a unit circle.

Step 2: Now draw a tangent and solve equation with the help of Pythagoras theorem.

In mathematical geometry, Equation of circle (unit) is given by: i2 + j2 = 1, here ‘i’ plot the coordinate value along to x – axis and ‘j’ plot the coordinate value along to y – axis.

Now we will discuss the table based on circle. The table is shown below:

s.no	Ó¨ (rad)	Ó¨0	Sin Ó¨	Cos Ó¨	tanÓ¨ = sinÓ¨ / cos Ó¨
1	0 Л / 6	0 30	√0 / 2 = 0 √1 / 2 = 1 / 2	√4 / 2 = 1 √3 / 2	√0 / √4 = 0 √1 / √3 = √3 / 3
2	Л / 3	60	√3 / 2	√1 / 2 = 1 / 2	√3 / √1 = √3
3	Л / 2	90	√4 / 2 = 1	√0 / 2 = 0	----

Using these value we can solve any problem related to unit circle.

Some properties are also based on circle which are given as:

Distance assess from center of circle to any point on a circle is radius of circle. Radius is always half of diameter.

Line that is passing passes through center of circle is diameter of circle. Diameter of circle is always twice the radius value of circle.

Circumference – Formula to calculate circumference of circle is given by: Circumference of circle = 2 лR.

By using Properties of Multiplication we can easily solve the mathematical problems. cbse syllabus for class 9th 2013 is useful for class 9^th student.