A **unit circle** is a circle whose radius = 1 unit and center is (0,0). Angles measured in clockwise will have positive values and angles measured in anticlockwise will
have negative values.

On unit circle, trigonometric functions are given as,

**X = Cos`theta` and Y = sin `theta`**

The value of sine is on the y coordinate of the unit circle and value of cosine is on the x - coordinate of the unit circle. Using the unit circle, any trigonometric function value can be calculated by using certain formulas. We can divide the unit circle into 4 quadrants.

We can easily make note of some angles by looking at the unit circle.

Y = sin`theta` and X = cos `theta`

Therefore, cos 0^{o} = 1 sin0^{o}= 0

cos 30^{o} = `sqrt(3)` /2 sin30^{o} = 1/2

cos 45^{o} = `sqrt(2)` /2 sin45^{o} = `sqrt(2)` /2

cos 90^{o} =
0 sin 90^{o } = 1

With these angles, we can also calculate other angles like tan`theta` , csc`theta` , sec`theta` and cot`theta`

For example, to find the value of tan 215^{o}, we know tan`theta` = sin`theta` / cos `theta`

= -`sqrt(2)` /2 `//` - `sqrt(2)` /2

= 1

Similar way, many unknown angles can be found.

- In the first quadrant, from 0
^{o}- 90^{o}both cos and sin are positive. Hence, all trigonometric functions are positive. - In the second quadrant, only sin is positive. Hence, all trigonometric functions except sin and its inverse csc are negative.
- In the third quadrant, only tan is positive. Hence, all trigonometric functions except tan and its inverse cot are negative.
- In the fourth quadrant, cos and sec is positive rest all are negative.

**Example 1:**

Find the area of an unit circle?

**Solution:**

We know that for an unit circle

radius =1 and center is (0,0)

Area = `pi r^2`

Here r=1 and `pi` = 3.14

So the area of an unit circle is

`= pi r^2`

`= pi *1^2`

`= pi * 1`

`= pi`

`= 3.14`

**Example 2:**

Find the equation of an unit circle?

**Solution:**

We know that for an unit circle

radius =1 and center is (0,0)

the genaral equation of a circle isgiven by

`x^2 + y^2 = r^2`

here r =1

`x^2 + y^2 = 1`

This is the equation of an unit circle.