college trigonometry: circular functions

The circular functions are functions of an angle. They are important in the study of triangles and modeling periodic phenomena, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right triangle contai..

1. The reciprocal of cos q = 1/cos q = sec q . 2. The reciprocal of sin q = 1/sin q = cosec q . 3. The reciprocal of tan q = 1/tan q = cot q..

\ The Circular function of a real number q and the trigonometric function for the angle q c are same. The identities for circular functions of real numbers hold for trigonometric functions of angle q..

The circle whose radius is 1 unit whose centre is the origin of a rectangular co-ordinate system is called the unit circle. 1. cos q = x. 2. sin q = y. 3. tan q = y/x. 4. sec q = 1/x. 5. cosec q = 1/y. 6. cot q = x/y. The six functions of q defined by the above equation are..

(i) sin(A + B) sin(A - B) = sin 2 A - sin 2 B = cos 2 B - cos 2 A (ii) cos(A + B) cos(A - B) = cos 2 A - sin 2 B = cos 2 B - sin 2 A [The proofs of the above identities are same as for Circular functions..

The following results have already been derived under Circular function..

The six functions of q defined by the above equation are called trigonometric functions of q or circular functions of q . Now consider the unit circle of radius 1 unit. Then the circumference is 2 p . If a moving point A starts from A and travel in the counte..

A radian is the measure of an angle at the centre of a circle subtended by an arc, whose arc length is equal to the radius of the circl..

The trigonometric functions belong to a large class of functions called periodic functions in which there is a regular repetition of the values of the function over a certain interv..

The trigonometric functions belong to a large class of functions called periodic functions in which there is a regular repetition of the values of the function over a certain interva..