Summary Physics all chapter's notes for class 11. | Most important

Important notes for Class XI
Students
For CBSE / WBBSE Boards




Physic notes from
Chapter 1 to 25

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Physics HandBook CH APTER




TRI GONOMETRY

2 radian = 360°  1 rad = 57.3°
perpendic ular base perpendicular
sin   cos =  tan =
hypoten use hypoten use base
a 2+b 2
base hypotenus e hypoten use a
cot = sec = cosec  =
perpendi cular base perpendi cular

a b a b
sin = cos = tan  =
a 2  b2 2
a b 2 b
1 1 1
cosec  = sec = cot  =
sin  cos  tan 
sin 2  + cos 2  = 1 1 + tan 2  = sec 2  1 + cot 2  = cosec 2 
90°
sin(A±B) = sinAcosB  cosAsinB cos(A±B) = cosAcosB  sinAsinB II I

tan A  tan B S in All
tan A  B   sin2A = 2sinAcosA 0°
1  tan A tan B 180° 360°
cos2A = cos 2 A–sin 2 A = 1–2sin 2 A = 2c os 2 A–1 T an C os
2 tan A III IV
tan2 A  sin3  = 3sin  – 4sin 3 
1  tan 2 A EN 270°
cos3  = 4c os 3  – 3c os 2sinAsinB = cos(A–B) – cos(A+B)
2cosAcosB = cos(A–B) + cos(A+B) 2sinAcosB = sin(A+B) + sin(A–B)


0° 30° 45° 60° 90° 120° 135° 150° 180° 270° 360°
 (0) /6) /4) /3) /2) /3) /4) /6)  /2) )
1 1 3 3 1 1
LL
sin  0 1 0 1 0
2 2 2 2 2 2
3 1 1 1 1 3
cos  1 0    -1 0 1
2 2 2 2 2 2
1 1
tan  0 1 3   3 -1  0  0
3 3
A


sin (90 ° + ) = c os  sin (180° – ) = sin  sin (– = –sin  sin (90° – ) = cos 
cos (90°+ ) = –sin  cos (180° – ) =– cos  cos (–) = cos  cs 90° – ) = sin 
tan (90°+ ) =– cot  tan(180°– ) =– tan  tan (–) = – tan  tan(90°– ) = cot 

sin (18 0° + ) = – sin  sin (270°– ) = – cos  sin (27 0°+ ) = – cos  sin (360°– ) = – sin 
cos (180° + ) = – cos  cos(270° – )= – sin  cos (270° + ) = sin  cos (360° – ) = cos 
tan (180° + ) = tan  tan (270° – ) = cot  tan (270° + ) = – cot  tan (360° – ) = – tan 


A
sine law For smal l 
A sin   cos   1 tan    sin  tan 
c b
sin A sinB sinC
 
B C
a b c
B C
a

cosine law
2 2 2
b +c -a c 2 + a 2 - b2 a 2 + b 2 - c2
cos A  , cosB  , cos C 
2bc 2ca 2a b
2 E

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Differentiat ion Maxima & Minima  of a function y=f(x)
dy dy 1
• yx 
n
 nx n 1 • y  nx   dy d2 y
dx dx x • For maximum value 0&   ve
dx dx 2
dy dy
• y  sin x   cos x • y  cos x    sin x dy d2 y
dx dx • For minimum value 0&   ve
dx dx 2
x  dy dy dv du
• ye   e x  • y  uv  u v
dx dx dx dx
Average o f a varying quantity
dy df  g  x   d  g  x  
• y  f  g  x    x2 x2
dx dg  x  dx
dy
 ydx
x1
 ydx
x1
• y=k(const ant)  0 If y = f(x) then  y   y  x2

dx x 2  x1
du dv
 dx
x1
v u
• y  u  dy  dx dx
v dx v2

Integration EN
C = Arbitrary constant, k = constant

•  f(x)dx  g(x) C

d
• (g(x))  f(x)
dx

•  kf(x)dx  k f(x)dx
LL

•  (u  v  w)dx   udx   vdx   wdx

•  e x dx  e x  C

x n 1
•  x n dx   C,n  1
A


n 1
1
•  dx  nx  C
x

•  sin xdx   cos x  C

•  cos xdx  sin x  C

1 x 
•  e x  dx  e C

n  x   n 1
•  x   dx   n  1 
C

Definite integration
b
b
 f(x)dx 
a
g(x)a  g(b)  g(a)

Area under the curve y = f(x) from x =a to a = b is
b
A   f(x)dx
a



E 3

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FORMULAE FOR DETERMINATION OF AREA
FO RMULAE FOR
• Area of a square = (side) 2 DETERMINATION OF
• Area of rectangle = length ×breadth VOLUME
1
• Area of a triangle = ×base × height t
2
• Area of a trapezoid a
1
= × (distance between parallel sides) × (sum of parallel sides) b
2
• Area enclosed by a circle = r2 (r = radius) • Volume of a rectangular
• Surface area of a sphere = 4 r2 (r = radius) slab
• Area of a parallelogram = base × height = length × breadth × height
• Area of curved surface of cylinder = r = abt
where r = radius and  = length
• Volume of a cube = (side) 3

• Area of whole surface of cylinder = 2 r (r + ) where  = length
• Area of ellipse =  ab 4 3
• Volume of a sphere = r
(a & b are semi major and semi minor axis respectively) 3

• Surface area of a cube = 6(side) 2 EN (r = radius)
• Tot al surface area of a cone = r2 + r • Volume of a cylinder = r2 
(r = radius and  = length)
where r = r r 2  h 2 = lateral area
• Arc length s = r.  r
1
• Volume of a cone = r2 h
3
r2 
• Area of sector =  s (r = radius and h = height)
2
LL
s r
• Plane angle,   radian
r

A
• Solid angle,   steradian
r2
A



• To convert an angle from degree to radian, we have to multiply it by and to convert an angle
180 

180 
from radian to degree, we have to multiply it by .



dy dy
KEY POINTS




• By help of differentiation, if y is given, we can find and by help of integration, if is given,
dx dx
we can find y.

• The maximum and minimum values of function

A cos   B sin  are A2  B2 and  A2  B2 respectively.

• (a+b)2 = a 2 + b 2 + 2ab (a–b)2 = a 2 + b 2 – 2ab

(a+b) (a–b) = a 2 – b 2 (a+b)3 = a 3 + b 3 + 3ab (a+b)

(a–b)3 = a 3 – b 3 – 3ab (a–b)

4 E