preparation for 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..

Which of the following represents the volume V of a right circular cone as a function of the radius r of its circular base, when the height of the cone is twice the radius of the base circle? => 2 π r 3 or 1 3 π r 3 or 2 3 π r 3 or 4 3 π r 3..

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..

Suppose a body is undergoing circular motion about a circle of radius r, with an angular velocity w rad/s as shown in the figure. From geometry, we can observe that the corresponding distance travelled in 1 second is equal to r w . Since the distance travelled in 1 second is velocity, ..

When things are arranged in places along a line with first and last place, they form a linear permutation. So far we have dealt only with linear permutations. When things are arranged in places along a closed curve or a circle, in which any place may be regarded as the first or last place, th..

In the example discussed under the topic uniform and non-uniform motion we have classified motion along circular track as an example of non-uniform motion. Let us now see why circular motion is considered as non-uniform motion. The figure shows an athlete running with uniform sp..

Circular Permutations - When things are arranged in places along a line with first and last place, they form a linear permutation. So far we have dealt only with linear permutations. When things are arranged in places along a closed curve or a circle, in which any place may be regarded as..

When things are arranged in places along a line with first and last place, they form a linear permutation. So far we have dealt only with linear permutations. When things are arranged in places along a closed curve or a circle, in which any place may be regarded as the first or last place, they for..