cosecant

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..

Summary - sin A = cos (90 o - A) tan A . tan (90 o - A) = 1 sin 2 A + cos 2 A = 1 1 + tan 2 A = sec 2 A 1 + cot 2 A = cosec 2..

Evaluate ∫ 6 cos 3 7 x + 7 sin 3 7 x 8 sin 2 7 x cos 2 7 x d x . => - 3 4 cosec 7 x + 7 8 sec 7 x + C or - 3 28 cosec 7 x - 1 8 sec 7 x + C or 3 4 cosec 7 x + 7 8 sec 7 x + C or..

Evaluate ∫ 3 cos 3 4 x - 4 sin 3 4 x 5 sin 2 4 x cos 2 4 x d x . => 3 20 cosec 4 x + 1 5 sec 4 x + C or 3 20 cosec 4 x - 1 5 sec 4 x + C or - 3 20 cosec 4 x - 1 5 sec 4 x + C or..

Identify the equation of the graph. => y = 2sec θ - 1 or y = 2sec θ + 1 or y = sec θ - 1 or y = 2cosec θ - 1..

In the principle value branches, the following formulae holds: - sin -1 (sin x) = x - cos -1 (cos x) = x - tan -1 (tan x) = x - cos -1 (cot x) = x - sec -1 (secx) = x - cosec -1 (cosecx) = x - sin -1 (-x) = -sin -1 x - cos -1 (-x) = p - cos -1 ..

Evaluate ∫ cos 7 x 1 + cos 7 x d x . => cosec 7 x + 1 7 cot 7 x + x + C or - 1 7 cosec 7 x + 1 7 cot 7 x + x + C or 1 7 cot 7 x + x + C or 1 7 cosec 7 x..

Evaluate : ∫ cos e c 4 x cos e c 4 x - cot 4 x d x => 4cot 4 x + 4cosec 4 x + C or - cot 4 x 4 - cos e c 4 x 4 + C or - 4cot 4 x - 4cosec 4 x + C or cot 4 x 4 + cos e c 4 x 4 + C..

Evaluate : ∫ 1 1 - cos 2 x d x => 2cosec 2 x + 2cot 2 x + C or - cos e c 2 x 2 - cot 2 x 2 + C or cos e c 2 x 2 + cot 2 x 2 + C or - 2cosec 2 x - 2cot 2 x + C..

Find the derivative of tan x . => - sec 2 x or - cos e c 2 x or sec 2 x or sec x cosec x..