# Sine Cosine Tangent by tutorcircleteam

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Sine Cosine Tangent

Trigonometry is a mathematical branch where, we study about triangle and their
relationships with sides and angle.

In trigonometry, we define functions with respect to triangle and some main
functions of trigonometry are sine cosine tangent.· sin x = opposite hypotenuse ·
cos x = adjacent hypotenuse · tan x = opposite adjacent Now, we discuss
derivatives of sine cosine tangent:

1. Derivative of sine: derivative of sin x is cos x.
D (sin x) = cos x
Dx 2. Derivative of cosine: derivative of cos x is –sin x D (cos x) = -sin x
Dx 3. Derivative of tangent: derivative of tan x is sec2 x. D (tan x) = sec2 x Dx
If, u = f(x) is a function of x,
then we define derivation of sine cosine and tangent by chain rule: a) Derivative
of sin u: Derivative of sin u is multiplication of cos u and Du/Dx D (sin u) = cos u
. Du Dx Dx b) Derivative of cos u: Derivative of cos u is multiplication of –sin u
and Du/Dx D (cos u) = -sin u .

Du Dx Dx c) Derivative of tan u : derivative of tan u is multiplication of sec2 u
and Du/Dx (tan u) = sec2 u . Du Dx x Now, we take different examples to
understand derivatives of sine cosine tangent:

1. Find derivative of y where y = sin(x2 + 3) y = D (sin (x2 + 3)) = cos (x2 + 3) .
D (x2 + 3) = cos (x2 + 3) . (2x) Dx Dx Dx 2. Find derivative of y where y = cos
3x4     Dy = D (cos 3x4) = -sin 3x4 .

D (3x4) = -sin 3x4 . 3(4x3) = 12x3.sin 3x4 x Dx x
3. Find derivative of y where y = x.tan x    Dy = D (x.tan x) = x . D (tan x) + tan
x . D (x) = x.sec2 x + tan x
Dx Dx                 Dx                DX