Unit circle can be best remembered in terms of lengths and angles from different perspectives. Suppose we have a unit circle with center at Intersection Point of 'x' and y- axes. Its graph is given as:

Equation of unit circle is given as X

^{2}+ Y

^{2}= 1. For different angles we have different behaviors of equation according to following diagram: The equation of the unit circle is given as X

^{2}+ Y

^{2}= 1. For different angles we have different behaviors of the equation according to the following diagram:

1. At 45 degrees, Y = X

X

^{2}+ X

^{2}= 1,

2X

^{2}= 1,

X

^{2}= 1 / 2,

X = Y = √ (1 / 2).

2. At 60 degrees all sides of triangle are equal: X = 1 / 2 And "Y" can be calculated as:

(1/2)

^{2}+ Y

^{2}= 1,

1/4 + Y

^{2}= 1,

Y

^{2}= 1 - 1/4 = ¾,

Y = √3/4.

3. At 30 degrees X= √3/4 and Y = ½.

According to pythagoras theorem we can write:

X

^{2}+ Y

^{2}= 12,

or X

^{2}+ Y

^{2}= 1,

Polar form coordinates of unit circle can be written as: X = cos A and Y = sin A. Substituting their values 'I' equation of the unit circle we get:

(cos(θ))

^{2}+ (sin(θ))

^{2}= 1 [It’s a very useful trigonometric identity].

For basic Trigonometric Functions cosine, sine and Tangent we define the value of Functions at some known angle as:

Angle |
Sine |
Cosine |
Tangent |

30 |
½ |
√3 / 2 |
1/√3 |

45 |
1/√2 |
1/√2 |
1 |

60 |
√3 / 2 |
½ |
√3 |