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# Points to Remember: Trigonometry & Its Application Class 10 Notes | EduRev

## Class 10 : Points to Remember: Trigonometry & Its Application Class 10 Notes | EduRev

``` 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 ?
=
Opposite
cot ?
=
Hypotenuse
sec ?
=
Opposite
tan ?
=
Hypotenuse
cos ?
=
Hypotenuse
b
a
c
Opp
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
Hypotenuse
Cos =
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 ?
=
Opposite
cot ?
=
Hypotenuse
sec ?
=
Opposite
tan ?
=
Hypotenuse
cos ?
=
Hypotenuse
b
a
c
Opp
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
Hypotenuse
Cos =
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
Dened
Not
Dened
Not
Dened
Not
Dened
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 ?
=
Opposite
cot ?
=
Hypotenuse
sec ?
=
Opposite
tan ?
=
Hypotenuse
cos ?
=
Hypotenuse
b
a
c
Opp
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
Hypotenuse
Cos =
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
Dened
Not
Dened
Not
Dened
Not
Dened
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.

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.
```
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## Mathematics (Maths) Class 10

51 videos|346 docs|103 tests

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