basic functions of trigonometry

Other Circular Functions (Reciprocal functions of cos , sin and tan)..

Periodic Functions - 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 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 containing the a..

i) A function f(x) is said to be even if f(-x) = f(x). ii) A function f(x) is said to be odd if f(-x) = -f(x..

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) A function f(x) is said to be even if f(-x) = f(x) ii) A function f(x) is said to be odd if f(-x) = -f(x) e.g., f(x) = x 3 , f(-x) = (-x) 3 = -x 3 = -f(x) f(x) = cos x is even for f(-x) = cos (-x) = cos q = f(x) f(x) = x cos x is odd for f(-x) = (-x) cos (-x) = -x cos x = -f(..

Definition - The figure is a unit circle, with origin O as centre cuts the x-axis at A (1,0) and let a variable point moving on the circumference move through an arc length q . i.e., AP = p( q ). The coordinates at the position of p( q ) are p(x,y) = (cos q , sin q ). Then the tangent function..

Theorem ..

The inverse function arsinhx, artanhx, arcschx and arcothx exist for all x (-, ) while arcoshx and arsechx exist only for x (0, ..

- 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..