Summary List of Formulas for Trigonometry, Differentiation and Integration

St. Xavier’s College (Autonomous), Ahmedabad - 380009
(Affiliated to Gujarat University)

Some Important Formulae and Results in
Trigonometry, Differentiation, Integration



1 Trigonometry
Consider a circle of radius 1 and centered at origin (unit circle).




Let P (a, b) be any point on the circle with angle AOP = x radian. We define cosx = a and
sinx = b. Since ∆OM P is a right angled triangle, we have OM 2 + M P 2 = 1 or a2 + b2 = 1. Thus,
we have the Pythagorean identity:
cos2 x + sin2 x = 1


1

, Other trigonometric functions are given by:
sin x
ˆ tan x =
cos x
1
ˆ csc x =
sin x
1
ˆ sec x =
cos x
cos x 1
ˆ cot x = =
sin x tan x
Some identities obtained from Pythagorean identity are:
ˆ 1 + tan2 x = sec2 x

ˆ 1 + cot2 x = csc2 x

Values of trigonometric functions for some standard values is given in the following table:




Signs of trigonometric functions in different quadrants can be given by: given in the following table:




Some basic trigonometric identities are listed below:
1. sin(−x) = − sin x, i.e. sine is an odd function.

2. cos(−x) = cos x, i.e. cosine is an even function.
π 
3. cos − x = sin x
2
π 
4. sin − x = cos x
2
2