All Courses
Get the App Signup / Login
Sign in Open App
JEE Exam  >  JEE Notes  >  Physics for JEE Main & Advanced  >  Important Formulas: Trigonometric Ratios, Functions and Equations

Important Formulas: Trigonometric Ratios, Functions and Equations | Physics for JEE Main & Advanced PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


.
 
Trigonometrical Ratios & Identities
1. Basic Trigonometric Identities:
(A) sin²
?
? + cos²
?
?  = 1;  ?1 ? sin ? ? 1;  ?1 ? cos ? ? 1  ? ? ? ? R
(B) sec²
?
? ? tan²
?
?  = 1  ;  ?sec
 
? ? ? 1   ??  ? ? R – ? ?
?
?
?
?
?
?
? ?
?
? n ,
2
1 n 2
(C) cosec²
?
? ? cot²
?
? = 1  ;  ?cosec
 
? ? ? 1  ?  ? ? R – ? ? ? ? ? n , n
2. Circular Definition Of Trigonometric Functions:
sin ? =
OP
P M
cos ? = 
OP
OM
tan ? =
?
?
cos
s i n
, cos ? ? ? 0
cot ? =
?
?
s i n
cos
, sin ? ? ? 0
sec ? =
? cos
1
, cos ? ? ? 0cosec ? =
? s i n
1
, sin ? ? ? 0
3. Trigonometric Functions Of Allied Angles:
If ? is any angle, then ? ? ? ? 90 ± ?, 180 ± ?, 270 ± ?, 360 ± ? etc. are called ALLIED ANGLES.
(A) sin ( ? ?) = ? sin
 
? ; cos ( ? ?) = cos
 
?
(B)  sin (90° ? ?) = cos
 
? ;cos (90°
 
? ?) = sin
 
?
(C)  sin (90° + ?) = cos
 
? ;cos (90° + ?) = ? sin
 
?
(D)  sin (180° ? ?) = sin
 
? ;cos (180° ? ?) = ? cos
 
?
(e)  sin (180° + ?) = ? sin
 
? ;cos (180° + ?) = ? cos
 
?
Page 2


.
 
Trigonometrical Ratios & Identities
1. Basic Trigonometric Identities:
(A) sin²
?
? + cos²
?
?  = 1;  ?1 ? sin ? ? 1;  ?1 ? cos ? ? 1  ? ? ? ? R
(B) sec²
?
? ? tan²
?
?  = 1  ;  ?sec
 
? ? ? 1   ??  ? ? R – ? ?
?
?
?
?
?
?
? ?
?
? n ,
2
1 n 2
(C) cosec²
?
? ? cot²
?
? = 1  ;  ?cosec
 
? ? ? 1  ?  ? ? R – ? ? ? ? ? n , n
2. Circular Definition Of Trigonometric Functions:
sin ? =
OP
P M
cos ? = 
OP
OM
tan ? =
?
?
cos
s i n
, cos ? ? ? 0
cot ? =
?
?
s i n
cos
, sin ? ? ? 0
sec ? =
? cos
1
, cos ? ? ? 0cosec ? =
? s i n
1
, sin ? ? ? 0
3. Trigonometric Functions Of Allied Angles:
If ? is any angle, then ? ? ? ? 90 ± ?, 180 ± ?, 270 ± ?, 360 ± ? etc. are called ALLIED ANGLES.
(A) sin ( ? ?) = ? sin
 
? ; cos ( ? ?) = cos
 
?
(B)  sin (90° ? ?) = cos
 
? ;cos (90°
 
? ?) = sin
 
?
(C)  sin (90° + ?) = cos
 
? ;cos (90° + ?) = ? sin
 
?
(D)  sin (180° ? ?) = sin
 
? ;cos (180° ? ?) = ? cos
 
?
(e)  sin (180° + ?) = ? sin
 
? ;cos (180° + ?) = ? cos
 
?
(f)  sin (270° ? ?) = ? cos
 
? ;cos (270° ? ?) = ? sin
 
?
(g)  sin (270° + ?) = ? cos
 
? ;cos (270° + ?) = sin
 
?
(h)  tan (90° ? ? ?) = cot
 
? ;cot (90° ? ? ?) = tan
 
?
4. Graphs of Trigonometric functions:
(A)  y = sin x x ? R;  y ? [–1, 1]
(B)  y = cos x x ? R;  y ? [ – 1, 1]
(C)  y = tan x   x ? R – (2n + 1) ? ?/2, n ?? ? ;  y ? R
(D)  y = cot x  x ? R – n ? , n ?? ?;  y ? R
(e)  y = cosec xx ? R  – n ? , n ?? ? ;  y ? ( ? ? ?, ? 1] ? [1, ?)
Page 3


.
 
Trigonometrical Ratios & Identities
1. Basic Trigonometric Identities:
(A) sin²
?
? + cos²
?
?  = 1;  ?1 ? sin ? ? 1;  ?1 ? cos ? ? 1  ? ? ? ? R
(B) sec²
?
? ? tan²
?
?  = 1  ;  ?sec
 
? ? ? 1   ??  ? ? R – ? ?
?
?
?
?
?
?
? ?
?
? n ,
2
1 n 2
(C) cosec²
?
? ? cot²
?
? = 1  ;  ?cosec
 
? ? ? 1  ?  ? ? R – ? ? ? ? ? n , n
2. Circular Definition Of Trigonometric Functions:
sin ? =
OP
P M
cos ? = 
OP
OM
tan ? =
?
?
cos
s i n
, cos ? ? ? 0
cot ? =
?
?
s i n
cos
, sin ? ? ? 0
sec ? =
? cos
1
, cos ? ? ? 0cosec ? =
? s i n
1
, sin ? ? ? 0
3. Trigonometric Functions Of Allied Angles:
If ? is any angle, then ? ? ? ? 90 ± ?, 180 ± ?, 270 ± ?, 360 ± ? etc. are called ALLIED ANGLES.
(A) sin ( ? ?) = ? sin
 
? ; cos ( ? ?) = cos
 
?
(B)  sin (90° ? ?) = cos
 
? ;cos (90°
 
? ?) = sin
 
?
(C)  sin (90° + ?) = cos
 
? ;cos (90° + ?) = ? sin
 
?
(D)  sin (180° ? ?) = sin
 
? ;cos (180° ? ?) = ? cos
 
?
(e)  sin (180° + ?) = ? sin
 
? ;cos (180° + ?) = ? cos
 
?
(f)  sin (270° ? ?) = ? cos
 
? ;cos (270° ? ?) = ? sin
 
?
(g)  sin (270° + ?) = ? cos
 
? ;cos (270° + ?) = sin
 
?
(h)  tan (90° ? ? ?) = cot
 
? ;cot (90° ? ? ?) = tan
 
?
4. Graphs of Trigonometric functions:
(A)  y = sin x x ? R;  y ? [–1, 1]
(B)  y = cos x x ? R;  y ? [ – 1, 1]
(C)  y = tan x   x ? R – (2n + 1) ? ?/2, n ?? ? ;  y ? R
(D)  y = cot x  x ? R – n ? , n ?? ?;  y ? R
(e)  y = cosec xx ? R  – n ? , n ?? ? ;  y ? ( ? ? ?, ? 1] ? [1, ?)
(f)  y = sec x x ? ? R – (2n + 1) ? ?/2, n ?? ? ;  y ? ( ? ? ?, ? 1] ? [1, ?)
5. Trigonometric Functions of Sum or Difference of Two Angles:
(A) sin (A ± B) = sinA cosB ± cosA sinB
(B) cos (A ± B) = cosA cosB ? sinA sinB
(C) sin²A ? sin²B = cos²B ? cos²A = sin (A+B). sin (A ? B)
(D) cos²A ? sin²B = cos²B ? sin²A = cos (A+B). cos (A
 
? B)
(e) tan
 
(A ± B) = 
B tan A tan 1
B tan A tan
?
?
(f) cot (A ± B) =
A cot B cot
1 B cot A cot
?
?
(g) tan (A + B + C)
=
A tan C tan C tan B tan B tan A tan 1
C tan B tan A tan C tan B tan A tan
? ? ?
? ? ?
.
6. Factorisation of the Sum or Difference of Two Sines or Cosines:
(A) sinC + sinD = 2 sin
2
D C ?
 cos
2
D C ?
(B) sinC ? sinD = 2 cos
2
D C ?
 sin
2
D C ?
(C) cosC + cosD = 2 cos
2
D C ?
 cos
2
D C ?
(D) cosC
 
?
 
cosD = ?
 
2 sin
2
D C ?
 
sin
2
D C ?
7. Transformation of Products into Sum or Difference of Sines & Cosines:
(A) 2 sinA cosB = sin(A+B) + sin(A ?B)
(B) 2 cosA sinB = sin(A+B) ? sin(A ?B)
(C) 2 cosA cosB = cos(A+B) + cos(A ?B)
(D) 2 sinA sinB = cos(A ?B) ? cos(A+B)
8. Multiple and Sub-multiple Angles :
(A) sin 2A = 2 sinA cosA ;  sin
 
? = 2 sin
?
2
 cos
?
2
(B) cos 2A = cos²A ? sin²A = 2cos²A
 
?
 
1 = 1 ? 2 sin²A;
Page 4


.
 
Trigonometrical Ratios & Identities
1. Basic Trigonometric Identities:
(A) sin²
?
? + cos²
?
?  = 1;  ?1 ? sin ? ? 1;  ?1 ? cos ? ? 1  ? ? ? ? R
(B) sec²
?
? ? tan²
?
?  = 1  ;  ?sec
 
? ? ? 1   ??  ? ? R – ? ?
?
?
?
?
?
?
? ?
?
? n ,
2
1 n 2
(C) cosec²
?
? ? cot²
?
? = 1  ;  ?cosec
 
? ? ? 1  ?  ? ? R – ? ? ? ? ? n , n
2. Circular Definition Of Trigonometric Functions:
sin ? =
OP
P M
cos ? = 
OP
OM
tan ? =
?
?
cos
s i n
, cos ? ? ? 0
cot ? =
?
?
s i n
cos
, sin ? ? ? 0
sec ? =
? cos
1
, cos ? ? ? 0cosec ? =
? s i n
1
, sin ? ? ? 0
3. Trigonometric Functions Of Allied Angles:
If ? is any angle, then ? ? ? ? 90 ± ?, 180 ± ?, 270 ± ?, 360 ± ? etc. are called ALLIED ANGLES.
(A) sin ( ? ?) = ? sin
 
? ; cos ( ? ?) = cos
 
?
(B)  sin (90° ? ?) = cos
 
? ;cos (90°
 
? ?) = sin
 
?
(C)  sin (90° + ?) = cos
 
? ;cos (90° + ?) = ? sin
 
?
(D)  sin (180° ? ?) = sin
 
? ;cos (180° ? ?) = ? cos
 
?
(e)  sin (180° + ?) = ? sin
 
? ;cos (180° + ?) = ? cos
 
?
(f)  sin (270° ? ?) = ? cos
 
? ;cos (270° ? ?) = ? sin
 
?
(g)  sin (270° + ?) = ? cos
 
? ;cos (270° + ?) = sin
 
?
(h)  tan (90° ? ? ?) = cot
 
? ;cot (90° ? ? ?) = tan
 
?
4. Graphs of Trigonometric functions:
(A)  y = sin x x ? R;  y ? [–1, 1]
(B)  y = cos x x ? R;  y ? [ – 1, 1]
(C)  y = tan x   x ? R – (2n + 1) ? ?/2, n ?? ? ;  y ? R
(D)  y = cot x  x ? R – n ? , n ?? ?;  y ? R
(e)  y = cosec xx ? R  – n ? , n ?? ? ;  y ? ( ? ? ?, ? 1] ? [1, ?)
(f)  y = sec x x ? ? R – (2n + 1) ? ?/2, n ?? ? ;  y ? ( ? ? ?, ? 1] ? [1, ?)
5. Trigonometric Functions of Sum or Difference of Two Angles:
(A) sin (A ± B) = sinA cosB ± cosA sinB
(B) cos (A ± B) = cosA cosB ? sinA sinB
(C) sin²A ? sin²B = cos²B ? cos²A = sin (A+B). sin (A ? B)
(D) cos²A ? sin²B = cos²B ? sin²A = cos (A+B). cos (A
 
? B)
(e) tan
 
(A ± B) = 
B tan A tan 1
B tan A tan
?
?
(f) cot (A ± B) =
A cot B cot
1 B cot A cot
?
?
(g) tan (A + B + C)
=
A tan C tan C tan B tan B tan A tan 1
C tan B tan A tan C tan B tan A tan
? ? ?
? ? ?
.
6. Factorisation of the Sum or Difference of Two Sines or Cosines:
(A) sinC + sinD = 2 sin
2
D C ?
 cos
2
D C ?
(B) sinC ? sinD = 2 cos
2
D C ?
 sin
2
D C ?
(C) cosC + cosD = 2 cos
2
D C ?
 cos
2
D C ?
(D) cosC
 
?
 
cosD = ?
 
2 sin
2
D C ?
 
sin
2
D C ?
7. Transformation of Products into Sum or Difference of Sines & Cosines:
(A) 2 sinA cosB = sin(A+B) + sin(A ?B)
(B) 2 cosA sinB = sin(A+B) ? sin(A ?B)
(C) 2 cosA cosB = cos(A+B) + cos(A ?B)
(D) 2 sinA sinB = cos(A ?B) ? cos(A+B)
8. Multiple and Sub-multiple Angles :
(A) sin 2A = 2 sinA cosA ;  sin
 
? = 2 sin
?
2
 cos
?
2
(B) cos 2A = cos²A ? sin²A = 2cos²A
 
?
 
1 = 1 ? 2 sin²A;
2 cos²
2
?
 = 1 + cos
 
?, 2 sin²
2
?
 = 1 ? cos
 
?.
(C) tan 2A =
A tan 1
A tan 2
2
?
; tan
 
? =
2
2
2
t an 1
t an 2
?
?
?
(D) sin 2A =
A tan 1
A tan 2
2
?
, cos 2A =
A tan 1
A tan 1
2
2
?
?
(e) sin 3A = 3 sinA
 
? 4 sin
3
A
(f) cos 3A = 4 cos
3
A ? 3 cosA
(g) tan 3A = 
A tan 3 1
A tan A tan 3
2
3
?
?
9. Important Trigonometric Ratios:
(A) sin n
 
? = 0 ; cos n
 
? = ( ?1)
n
;  tan n
 
? = 0,  where n ? ?
(B) sin 15° or  sin
12
?
  = 
2 2
1 3 ?
 = cos 75° or  cos 
12
5 ?
;
 cos 15° or  cos
12
?
  = 
2 2
1 3 ?
 = sin 75°  or  sin 
12
5 ?
;
tan
 
15° =
1 3
1 3
?
?
 = 3 2 ? = cot 75° ; tan
 
75° =
1 3
1 3
?
?
 = 3 2 ? = cot 15°
(C) sin
10
?
 or sin 18° =
4
1 5 ?
  &  cos 36° or cos
5
?
 = 
4
1 5 ?
10. Conditional Identities:
If  A + B + C = ?  then :
(i) sin2A + sin2B + sin2C = 4 sinA sinB sinC
(ii) sinA + sinB + sinC = 4 cos
2
A
 cos
2
B
 cos
2
C
(iii) cos 2
 
A + cos 2
 
B + cos 2
 
C = ? 1 ? 4 cos A cos B cos C
(iv) cos A + cos B + cos C = 1 + 4 sin
2
A
 sin
2
B
 sin
2
C
(v) tanA + tanB + tanC = tanA tanB tanC
(vi) tan
2
A
 tan
2
B
 + tan
2
B
 tan
2
C
 + tan
2
C
 tan
2
A
 = 1
(vii) cot
2
A
 + cot
2
B
 + cot
2
C
 = cot
2
A
. cot
2
B
. cot
2
C
(viii) cot A cot B + cot B cot C + cot C cot A = 1
(ix) A + B + C =
?
2
  then  tan A tan B + tan B tan C + tan C tan A = 1
Page 5


.
 
Trigonometrical Ratios & Identities
1. Basic Trigonometric Identities:
(A) sin²
?
? + cos²
?
?  = 1;  ?1 ? sin ? ? 1;  ?1 ? cos ? ? 1  ? ? ? ? R
(B) sec²
?
? ? tan²
?
?  = 1  ;  ?sec
 
? ? ? 1   ??  ? ? R – ? ?
?
?
?
?
?
?
? ?
?
? n ,
2
1 n 2
(C) cosec²
?
? ? cot²
?
? = 1  ;  ?cosec
 
? ? ? 1  ?  ? ? R – ? ? ? ? ? n , n
2. Circular Definition Of Trigonometric Functions:
sin ? =
OP
P M
cos ? = 
OP
OM
tan ? =
?
?
cos
s i n
, cos ? ? ? 0
cot ? =
?
?
s i n
cos
, sin ? ? ? 0
sec ? =
? cos
1
, cos ? ? ? 0cosec ? =
? s i n
1
, sin ? ? ? 0
3. Trigonometric Functions Of Allied Angles:
If ? is any angle, then ? ? ? ? 90 ± ?, 180 ± ?, 270 ± ?, 360 ± ? etc. are called ALLIED ANGLES.
(A) sin ( ? ?) = ? sin
 
? ; cos ( ? ?) = cos
 
?
(B)  sin (90° ? ?) = cos
 
? ;cos (90°
 
? ?) = sin
 
?
(C)  sin (90° + ?) = cos
 
? ;cos (90° + ?) = ? sin
 
?
(D)  sin (180° ? ?) = sin
 
? ;cos (180° ? ?) = ? cos
 
?
(e)  sin (180° + ?) = ? sin
 
? ;cos (180° + ?) = ? cos
 
?
(f)  sin (270° ? ?) = ? cos
 
? ;cos (270° ? ?) = ? sin
 
?
(g)  sin (270° + ?) = ? cos
 
? ;cos (270° + ?) = sin
 
?
(h)  tan (90° ? ? ?) = cot
 
? ;cot (90° ? ? ?) = tan
 
?
4. Graphs of Trigonometric functions:
(A)  y = sin x x ? R;  y ? [–1, 1]
(B)  y = cos x x ? R;  y ? [ – 1, 1]
(C)  y = tan x   x ? R – (2n + 1) ? ?/2, n ?? ? ;  y ? R
(D)  y = cot x  x ? R – n ? , n ?? ?;  y ? R
(e)  y = cosec xx ? R  – n ? , n ?? ? ;  y ? ( ? ? ?, ? 1] ? [1, ?)
(f)  y = sec x x ? ? R – (2n + 1) ? ?/2, n ?? ? ;  y ? ( ? ? ?, ? 1] ? [1, ?)
5. Trigonometric Functions of Sum or Difference of Two Angles:
(A) sin (A ± B) = sinA cosB ± cosA sinB
(B) cos (A ± B) = cosA cosB ? sinA sinB
(C) sin²A ? sin²B = cos²B ? cos²A = sin (A+B). sin (A ? B)
(D) cos²A ? sin²B = cos²B ? sin²A = cos (A+B). cos (A
 
? B)
(e) tan
 
(A ± B) = 
B tan A tan 1
B tan A tan
?
?
(f) cot (A ± B) =
A cot B cot
1 B cot A cot
?
?
(g) tan (A + B + C)
=
A tan C tan C tan B tan B tan A tan 1
C tan B tan A tan C tan B tan A tan
? ? ?
? ? ?
.
6. Factorisation of the Sum or Difference of Two Sines or Cosines:
(A) sinC + sinD = 2 sin
2
D C ?
 cos
2
D C ?
(B) sinC ? sinD = 2 cos
2
D C ?
 sin
2
D C ?
(C) cosC + cosD = 2 cos
2
D C ?
 cos
2
D C ?
(D) cosC
 
?
 
cosD = ?
 
2 sin
2
D C ?
 
sin
2
D C ?
7. Transformation of Products into Sum or Difference of Sines & Cosines:
(A) 2 sinA cosB = sin(A+B) + sin(A ?B)
(B) 2 cosA sinB = sin(A+B) ? sin(A ?B)
(C) 2 cosA cosB = cos(A+B) + cos(A ?B)
(D) 2 sinA sinB = cos(A ?B) ? cos(A+B)
8. Multiple and Sub-multiple Angles :
(A) sin 2A = 2 sinA cosA ;  sin
 
? = 2 sin
?
2
 cos
?
2
(B) cos 2A = cos²A ? sin²A = 2cos²A
 
?
 
1 = 1 ? 2 sin²A;
2 cos²
2
?
 = 1 + cos
 
?, 2 sin²
2
?
 = 1 ? cos
 
?.
(C) tan 2A =
A tan 1
A tan 2
2
?
; tan
 
? =
2
2
2
t an 1
t an 2
?
?
?
(D) sin 2A =
A tan 1
A tan 2
2
?
, cos 2A =
A tan 1
A tan 1
2
2
?
?
(e) sin 3A = 3 sinA
 
? 4 sin
3
A
(f) cos 3A = 4 cos
3
A ? 3 cosA
(g) tan 3A = 
A tan 3 1
A tan A tan 3
2
3
?
?
9. Important Trigonometric Ratios:
(A) sin n
 
? = 0 ; cos n
 
? = ( ?1)
n
;  tan n
 
? = 0,  where n ? ?
(B) sin 15° or  sin
12
?
  = 
2 2
1 3 ?
 = cos 75° or  cos 
12
5 ?
;
 cos 15° or  cos
12
?
  = 
2 2
1 3 ?
 = sin 75°  or  sin 
12
5 ?
;
tan
 
15° =
1 3
1 3
?
?
 = 3 2 ? = cot 75° ; tan
 
75° =
1 3
1 3
?
?
 = 3 2 ? = cot 15°
(C) sin
10
?
 or sin 18° =
4
1 5 ?
  &  cos 36° or cos
5
?
 = 
4
1 5 ?
10. Conditional Identities:
If  A + B + C = ?  then :
(i) sin2A + sin2B + sin2C = 4 sinA sinB sinC
(ii) sinA + sinB + sinC = 4 cos
2
A
 cos
2
B
 cos
2
C
(iii) cos 2
 
A + cos 2
 
B + cos 2
 
C = ? 1 ? 4 cos A cos B cos C
(iv) cos A + cos B + cos C = 1 + 4 sin
2
A
 sin
2
B
 sin
2
C
(v) tanA + tanB + tanC = tanA tanB tanC
(vi) tan
2
A
 tan
2
B
 + tan
2
B
 tan
2
C
 + tan
2
C
 tan
2
A
 = 1
(vii) cot
2
A
 + cot
2
B
 + cot
2
C
 = cot
2
A
. cot
2
B
. cot
2
C
(viii) cot A cot B + cot B cot C + cot C cot A = 1
(ix) A + B + C =
?
2
  then  tan A tan B + tan B tan C + tan C tan A = 1
 11. Range of Trigonometric Expression:
E = a sin
 
? + b cos
 
?
E =
2 2
b a ? sin ( ? + ?), where tan ? =
a
b
  =
2 2
b a ? cos (? ?? ??), where tan ? =
b
a
Hence for any real value of ? ?, 
2 2 2 2
ba E ba ? ? ? ? ?
12. Sine and Cosine Series:
sin
 
? + sin
 
( ??+ ? ?) + sin
 
( ? + 2 ? ) +...... + sin ? ? ? ? ? ? 1 n =
2
2
n
s i n
s i n
?
?
 sin
 
?
?
?
?
?
?
?
?
? ?
2
1 n
cos
 
? + cos
 
( ??+ ? ?) + cos
 
( ? + 2 ? ) +...... + cos ? ? ? ? ? ? 1 n =
2
2
n
s i n
s i n
?
?
 cos
 
?
?
?
?
?
?
?
?
? ?
2
1 n
 1. DEFINITION
The equations involving trigonometric function of unknown angles are known as Trigonometric equations
e.g.  cos ? = 0 , cos
2
? – 4cos ? =1 , sin
2
? + sin ? = 2 , cos
2
 ? – 4sin ? =1
A solution of a trigonometric equation is the value of the unknown angle that satisfies the equation.
e.g.,   
1 3 9 11
sin o r , , , .. . .. ....
4 4 4 4 4 2
? ? ? ? ?
? ? ? ? ? ? ?
 2. PERIODIC FUNCTION
A function f(x) is said to be periodic if there exists T > 0 such that f(x + T) = f(x) for all x in the domain of
definitions of f(x). If T is the smallest positive real numbers such that f(x + T) = f(x) , then it is called the period of
f(x)
Since sin (2n ? + x ) = sinx , cos (2n ? + x) = cos x     ;     tan (n ? + x) = tan x  for all  n ? Z
Therefore sinx , cosx and tanx are perodic function, the period of sinx and cos x is 2 ? and that of tanx is ? .
Function Period
sin (ax + b) , cos (ax +b), sec (ax + b) , cosec (ax +b ) 2 ?/a
tan (ax + b), cot (ax +b) ?/a
| sin (ax + b)| , | cos (ax +b) | , | sec (ax +b) | , | cosec (ax +b ) | ?/a
| tan (ax + b ) | , | cot (ax +b ) | ?/2a
Trigonometrical Equations
Read More
289 videos|635 docs|179 tests
Join Course for Free

Top Courses for JEE

FAQs on Important Formulas: Trigonometric Ratios, Functions and Equations - Physics for JEE Main & Advanced

1. What are the trigonometric ratios?
Ans. Trigonometric ratios are ratios of the sides of a right triangle with respect to its angles. The main trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). They are defined as follows: - Sine (sin) of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. - Cosine (cos) of an angle is equal to the ratio of the length of the adjacent side to the length of the hypotenuse. - Tangent (tan) of an angle is equal to the ratio of the length of the side opposite the angle to the length of the adjacent side.
2. How are trigonometric functions related to trigonometric ratios?
Ans. Trigonometric functions are mathematical functions that are defined based on the ratios of sides in a right triangle. The main trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions are defined as follows: - Sine (sin) of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. - Cosine (cos) of an angle is equal to the ratio of the length of the adjacent side to the length of the hypotenuse. - Tangent (tan) of an angle is equal to the ratio of the length of the side opposite the angle to the length of the adjacent side. - Cosecant (csc) of an angle is equal to the reciprocal of the sine of the angle. - Secant (sec) of an angle is equal to the reciprocal of the cosine of the angle. - Cotangent (cot) of an angle is equal to the reciprocal of the tangent of the angle.
3. How can trigonometric ratios be used to solve equations?
Ans. Trigonometric ratios can be used to solve equations involving trigonometric functions. By applying the trigonometric ratios and identities, we can manipulate the equations to find the values of the angles or sides involved. This is particularly useful in solving problems related to triangles, angles, and distances. The equations can be solved using algebraic techniques such as substitution, simplification, and factoring.
4. What are the important trigonometric identities to remember?
Ans. Some important trigonometric identities to remember are: - Pythagorean Identities: sin^2θ + cos^2θ = 1 and 1 + tan^2θ = sec^2θ. - Reciprocal Identities: cscθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ. - Quotient Identities: tanθ = sinθ/cosθ and cotθ = cosθ/sinθ. - Co-Function Identities: sin(π/2 - θ) = cosθ, cos(π/2 - θ) = sinθ, and tan(π/2 - θ) = cotθ. - Even-Odd Identities: sin(-θ) = -sinθ, cos(-θ) = cosθ, and tan(-θ) = -tanθ. - Double Angle Identities: sin(2θ) = 2sinθcosθ, cos(2θ) = cos^2θ - sin^2θ, and tan(2θ) = 2tanθ/1 - tan^2θ.
5. How can trigonometric ratios be applied in real-life scenarios?
Ans. Trigonometric ratios have various applications in real-life scenarios. Some examples include: - In navigation and surveying, trigonometric ratios are used to determine distances, angles, and heights of objects. - In physics and engineering, trigonometric ratios are used to analyze and calculate forces, velocities, and trajectories. - In architecture and construction, trigonometric ratios are used to design and build structures with specific angles and dimensions. - In astronomy, trigonometric ratios are used to calculate the positions and movements of celestial objects. - In sound and wave analysis, trigonometric ratios are used to study the properties of sound waves and analyze their frequencies and amplitudes.
Related Exams
JEE
About this Document
4.79/5 Rating
Dec 22, 2024 Last updated
Document Description: Important Formulas: Trigonometric Ratios, Functions and Equations for JEE 2024 is part of Physics for JEE Main & Advanced preparation. The notes and questions for Important Formulas: Trigonometric Ratios, Functions and Equations have been prepared according to the JEE exam syllabus. Information about Important Formulas: Trigonometric Ratios, Functions and Equations covers topics like and Important Formulas: Trigonometric Ratios, Functions and Equations Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Important Formulas: Trigonometric Ratios, Functions and Equations.
Introduction of Important Formulas: Trigonometric Ratios, Functions and Equations in English is available as part of our Physics for JEE Main & Advanced for JEE & Important Formulas: Trigonometric Ratios, Functions and Equations in Hindi for Physics for JEE Main & Advanced course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Important Formulas: Trigonometric Ratios, Functions and Equations | Physics for JEE Main & Advanced
Description
Full syllabus notes, lecture & questions for Important Formulas: Trigonometric Ratios, Functions and Equations | Physics for JEE Main & Advanced - JEE | Plus excerises question with solution to help you revise complete syllabus for Physics for JEE Main & Advanced | Best notes, free PDF download
Information about Important Formulas: Trigonometric Ratios, Functions and Equations
In this doc you can find the meaning of Important Formulas: Trigonometric Ratios, Functions and Equations defined & explained in the simplest way possible. Besides explaining types of Important Formulas: Trigonometric Ratios, Functions and Equations theory, EduRev gives you an ample number of questions to practice Important Formulas: Trigonometric Ratios, Functions and Equations tests, examples and also practice JEE tests
289 videos|635 docs|179 tests
Join Course for Free
Download as PDF
Explore Courses for JEE exam

Top Courses for JEE

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

ppt

,

study material

,

Important Formulas: Trigonometric Ratios

,

shortcuts and tricks

,

Extra Questions

,

Summary

,

Functions and Equations | Physics for JEE Main & Advanced

,

Viva Questions

,

Free

,

mock tests for examination

,

Exam

,

Functions and Equations | Physics for JEE Main & Advanced

,

Sample Paper

,

Objective type Questions

,

Important Formulas: Trigonometric Ratios

,

Important Formulas: Trigonometric Ratios

,

Important questions

,

pdf

,

practice quizzes

,

MCQs

,

Functions and Equations | Physics for JEE Main & Advanced

,

Semester Notes

,

past year papers

,

video lectures

,

Previous Year Questions with Solutions

;
Additional Information about Important Formulas: Trigonometric Ratios, Functions and Equations for JEE Preparation

Important Formulas: Trigonometric Ratios, Functions and Equations Free PDF Download

The Important Formulas: Trigonometric Ratios, Functions and Equations is an invaluable resource that delves deep into the core of the JEE exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the Important Formulas: Trigonometric Ratios, Functions and Equations now and kickstart your journey towards success in the JEE exam.

Importance of Important Formulas: Trigonometric Ratios, Functions and Equations

The importance of Important Formulas: Trigonometric Ratios, Functions and Equations cannot be overstated, especially for JEE aspirants. This document holds the key to success in the JEE exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Important Formulas: Trigonometric Ratios, Functions and Equations Notes

Important Formulas: Trigonometric Ratios, Functions and Equations Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Important Formulas: Trigonometric Ratios, Functions and Equations. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Important Formulas: Trigonometric Ratios, Functions and Equations Notes on EduRev are your ultimate resource for success.

Important Formulas: Trigonometric Ratios, Functions and Equations JEE Questions

The "Important Formulas: Trigonometric Ratios, Functions and Equations JEE Questions" guide is a valuable resource for all aspiring students preparing for the JEE exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Important Formulas: Trigonometric Ratios, Functions and Equations on the App

Students of JEE can study Important Formulas: Trigonometric Ratios, Functions and Equations alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Important Formulas: Trigonometric Ratios, Functions and Equations, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Important Formulas: Trigonometric Ratios, Functions and Equations is prepared as per the latest JEE syllabus.
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup