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..

Theorem ..

\ 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..

- 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 ) a..

(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..

According to wave mechanics, we cannot simply say that the electron exists at a particular point but we talk about certain regions in space around the nucleus where the probability of finding the electron is maximum. Such regions are expressed by mathematical expressions and are called orbita..

Trigonometric Ratios of Multiple and Sub-multiple Angles - The following results have already been derived under Circular function..

fig. 19.2 - Bacterial Chromosome In addition to the nucleoid, a bacterial cell may show the presence of extra chromosomal DNA molecules called plasmids. Like the bacterial chromosome, plasmids are double stranded circular DNA molecules which can replicate and function independen..