Points to Remember: Trigonometry & its Application | Mathematics (Maths) Class 10 PDF Download

 Page 1


Trigonometry  
And 
 its Application 
Page 2


Trigonometry  
And 
 its Application 
Trigonometric Identities
similarly
sin ?
 = 
cosec ?
1
cosec ?
 = 
sin ?
1
similarly cos ?
 = 
sec ?
1
sec ?
 = 
cos ?
1
Complementary Angles
sin ?
 = cos (90 - ?
) 
cosec ?
 = sec (90 - ?
) 
cos ?
 = sin (90 - ?
) 
sec ?
 = cosec (90 - ?
)
similarly
similarly
similarly
tan ?
 = cot (90 - ?
) 
cot ?
 = tan (90 - ?
) 
similarly tan ?
 = 
cot ?
1
cot ?
 = 
tan ?
1
sin
2
 ?
 + cos
2
 ?
 = 1 cosec
2
 ?
 - cot
2
 ?
 = 1 sec
2
 ?
 -  tan
2
 ?
 = 1
Trigonometric Ratios
Opposite
Hypotenuse
sin ?
 =
Opposite
Hypotenuse
cosec ?
 =
Adjacent
Opposite
cot ?
 =
Adjacent
Hypotenuse
sec ?
 =
Adjacent
Opposite
tan ?
 =
Adjacent
Hypotenuse
cos ?
 =
Hypotenuse
Adj
b
a
c
Opp
Adj
30
o
60
o
90
o
Opp
Useful Terms for Application of Trigonometry
Angle of elevation
(Line of sight)
Ground
Angle of depression
Horizontal line (Parallel to ground)
Ground
(90 -?)
?
?
?
(90 -?)
Opposite
Hypotenuse
Sin =
SOH
CAH
TOA
Adjacent
Hypotenuse
Cos =
Adjacent
Opposite
Tan =
TRIGONOMETRY & ITS APPLICATIONS 22
Trigonometry & its Applications
Page 3


Trigonometry  
And 
 its Application 
Trigonometric Identities
similarly
sin ?
 = 
cosec ?
1
cosec ?
 = 
sin ?
1
similarly cos ?
 = 
sec ?
1
sec ?
 = 
cos ?
1
Complementary Angles
sin ?
 = cos (90 - ?
) 
cosec ?
 = sec (90 - ?
) 
cos ?
 = sin (90 - ?
) 
sec ?
 = cosec (90 - ?
)
similarly
similarly
similarly
tan ?
 = cot (90 - ?
) 
cot ?
 = tan (90 - ?
) 
similarly tan ?
 = 
cot ?
1
cot ?
 = 
tan ?
1
sin
2
 ?
 + cos
2
 ?
 = 1 cosec
2
 ?
 - cot
2
 ?
 = 1 sec
2
 ?
 -  tan
2
 ?
 = 1
Trigonometric Ratios
Opposite
Hypotenuse
sin ?
 =
Opposite
Hypotenuse
cosec ?
 =
Adjacent
Opposite
cot ?
 =
Adjacent
Hypotenuse
sec ?
 =
Adjacent
Opposite
tan ?
 =
Adjacent
Hypotenuse
cos ?
 =
Hypotenuse
Adj
b
a
c
Opp
Adj
30
o
60
o
90
o
Opp
Useful Terms for Application of Trigonometry
Angle of elevation
(Line of sight)
Ground
Angle of depression
Horizontal line (Parallel to ground)
Ground
(90 -?)
?
?
?
(90 -?)
Opposite
Hypotenuse
Sin =
SOH
CAH
TOA
Adjacent
Hypotenuse
Cos =
Adjacent
Opposite
Tan =
TRIGONOMETRY & ITS APPLICATIONS 22
Trigonometry & its Applications
Trick To Remember Trigonometry Value Table
Step 1 : Write numbers 0-4
Divide them by 4
Take square root
0 1 2 3 4
0 1 2 3 4
4 4 4 4 4
Step 2 :
Step 3 :
Now we have the values for
sin ?
Step 4 :
Reverse the values of sin ? to
obtain the values for cos ? as
given in table.
Now cosec ? is inverse of sin ? & sec ? is inverse
of cos ?, so the values. Similarly value for tan ?
& cot ? can be obtained by using
Step 5 :
Step 6 :
0
0 1 2 3 4
4 4 4 4 4
1
2
1
3
2
1
2
cos ?
sin ?
sin ?
cos ?
 ,        cot ? = 
tan ? =
45
o
60
o
90
o
0
o
sin ?
?
Ratio
cos ?
cosec ?
sec ?
tan ?
cot ?
30
o
1
1
1
1
1
1
2
Not
Dened
Not
Dened
Not
Dened
Not
Dened
0
0
0
0
1
2
1
2
2
3
2
3
1
3
2
2 2
3
3
3
3
2
3
2
1
2
1
2
sin ? (0
o
, 30
o
, 45
o
, 60
o
, 90
o
)
TRIGONOMETRY & ITS APPLICATIONS 23
Page 4


Trigonometry  
And 
 its Application 
Trigonometric Identities
similarly
sin ?
 = 
cosec ?
1
cosec ?
 = 
sin ?
1
similarly cos ?
 = 
sec ?
1
sec ?
 = 
cos ?
1
Complementary Angles
sin ?
 = cos (90 - ?
) 
cosec ?
 = sec (90 - ?
) 
cos ?
 = sin (90 - ?
) 
sec ?
 = cosec (90 - ?
)
similarly
similarly
similarly
tan ?
 = cot (90 - ?
) 
cot ?
 = tan (90 - ?
) 
similarly tan ?
 = 
cot ?
1
cot ?
 = 
tan ?
1
sin
2
 ?
 + cos
2
 ?
 = 1 cosec
2
 ?
 - cot
2
 ?
 = 1 sec
2
 ?
 -  tan
2
 ?
 = 1
Trigonometric Ratios
Opposite
Hypotenuse
sin ?
 =
Opposite
Hypotenuse
cosec ?
 =
Adjacent
Opposite
cot ?
 =
Adjacent
Hypotenuse
sec ?
 =
Adjacent
Opposite
tan ?
 =
Adjacent
Hypotenuse
cos ?
 =
Hypotenuse
Adj
b
a
c
Opp
Adj
30
o
60
o
90
o
Opp
Useful Terms for Application of Trigonometry
Angle of elevation
(Line of sight)
Ground
Angle of depression
Horizontal line (Parallel to ground)
Ground
(90 -?)
?
?
?
(90 -?)
Opposite
Hypotenuse
Sin =
SOH
CAH
TOA
Adjacent
Hypotenuse
Cos =
Adjacent
Opposite
Tan =
TRIGONOMETRY & ITS APPLICATIONS 22
Trigonometry & its Applications
Trick To Remember Trigonometry Value Table
Step 1 : Write numbers 0-4
Divide them by 4
Take square root
0 1 2 3 4
0 1 2 3 4
4 4 4 4 4
Step 2 :
Step 3 :
Now we have the values for
sin ?
Step 4 :
Reverse the values of sin ? to
obtain the values for cos ? as
given in table.
Now cosec ? is inverse of sin ? & sec ? is inverse
of cos ?, so the values. Similarly value for tan ?
& cot ? can be obtained by using
Step 5 :
Step 6 :
0
0 1 2 3 4
4 4 4 4 4
1
2
1
3
2
1
2
cos ?
sin ?
sin ?
cos ?
 ,        cot ? = 
tan ? =
45
o
60
o
90
o
0
o
sin ?
?
Ratio
cos ?
cosec ?
sec ?
tan ?
cot ?
30
o
1
1
1
1
1
1
2
Not
Dened
Not
Dened
Not
Dened
Not
Dened
0
0
0
0
1
2
1
2
2
3
2
3
1
3
2
2 2
3
3
3
3
2
3
2
1
2
1
2
sin ? (0
o
, 30
o
, 45
o
, 60
o
, 90
o
)
TRIGONOMETRY & ITS APPLICATIONS 23 TRIGONOMETRY & ITS APPLICATIONS 24
         Convert all sec, cosec, cot, and tan into sin and cos, Most of this can be 
done using the quotient and reciprocal identities.
         Expand the equation if you can, combine like terms, and simplify the
equations.
Check for angle multiples and remove them using the appropriate 
        Just remember the Sin ? Value in trigonometry value table. Others 
can be derived easily. 
        For word problem: make proper diagrams by maintaining the aspect 
ratio of the angles and sides. Also, don’t get confused between angle of  
elevation and depression (most common mistake).
         For questions given in the radical form (Square root), try to rationalize 
it by multiplying the term in the numerator and in the denominator. 
         Just remember one identity Sin
2
 ? + Cos
2
 ? = 1. We can derive the 
other identities by just dividing this identity by Sin
2 
? & Cos
2 
? respectively. 
         While solving problems where you have to prove L.H.S = R.H.S, try to 
bring both the sides to the form of Sin ? and Cos ?. 
         Last but not the least, please remember all the formulae. 
PLEASE KEEP IN MIND
 
Introduction & Trigonometry Ratios
Amazing trick to understand 
trigonometry formula
Scan the QR Codes to watch our free videos
Application of trigonometry 
         
Simple Trick to remember
trigonometry value table 
         
  How to make clinometer 
How to use clinometer Board Questions Solved 
?
?
?
?
?
?
?
?
         Speed =  
         Time  
         , Use this formula in problems related to speed and 
           distance. 
         Distance  
?
?
formulas.