Trigonometric functions and it's properties

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Identical properties of circular functions and trigonometric functions.

Let O be the origin. Let OA be the unit radius of the circle drawn with O as centre. Let OA trace an angle when OA takes the position OP. Then

The tracing of the angle q and the arc AP = P(q) are one and the same.

Let the co-ordinates of P be (x, y).

Draw PM perpendicular to x-axis.

By the definition of Circular functions, we have

The Circular function of a real number  q and the trigonometric function for the angle q^c are same.

From the above property, the identities for circular functions of real numbers hold for trigonometric functions of angle q.