Points to Remember: Trigonometry & its Application

# 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 ?
=
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.
```

## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

## FAQs on Points to Remember: Trigonometry & its Application - Mathematics (Maths) Class 10

 1. What is trigonometry and how is it applied in real-life situations?
Ans. Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles, particularly right triangles. It involves the study of angles, sides, and trigonometric functions such as sine, cosine, and tangent. Trigonometry is widely used in various fields such as engineering, physics, architecture, and navigation. For example, it is used to calculate distances and heights, analyze wave patterns, design bridges and buildings, and navigate ships and airplanes.
 2. How do I calculate the value of trigonometric ratios for different angles?
Ans. To calculate the value of trigonometric ratios (sine, cosine, tangent) for different angles, you can use a scientific calculator or refer to trigonometric tables. However, if you want to calculate it manually, you can use the unit circle or right triangles. For example, to find the sine of an angle, divide the length of the side opposite to the angle by the length of the hypotenuse in a right triangle. Similarly, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.
 3. How can I solve trigonometric equations and find the values of unknown angles?
Ans. To solve trigonometric equations and find the values of unknown angles, you can use various trigonometric identities and properties. Some common methods include using the Pythagorean identity, sum and difference formulas, and double-angle formulas. Additionally, you can use inverse trigonometric functions (arcsine, arccosine, arctangent) to find the angles corresponding to given trigonometric ratios. Practice and familiarity with these formulas will help you efficiently solve trigonometric equations.
 4. What are the practical applications of trigonometry in the field of engineering?
Ans. Trigonometry plays a crucial role in engineering applications. It is used in structural analysis to calculate forces, stresses, and angles in various components of buildings and bridges. Trigonometry is also essential in electrical engineering for analyzing alternating currents and voltages, calculating phase angles, and designing circuit components. In mechanical engineering, trigonometry helps in designing gears, pulleys, and other mechanical systems. Overall, trigonometry helps engineers solve complex problems and make accurate calculations in their respective fields.
 5. How does trigonometry relate to navigation and astronomy?
Ans. Trigonometry is extensively used in navigation and astronomy. In navigation, trigonometric principles are applied to determine the position, distance, and direction of ships, airplanes, and satellites. Trigonometry helps in calculating angles of elevation and depression, which are crucial for determining the height of objects or landmarks. Similarly, in astronomy, trigonometry is used to measure distances between celestial objects, calculate the size and orbits of planets, and predict astronomical events such as eclipses. Without trigonometry, accurate navigation and understanding of celestial phenomena would be significantly challenging.

## Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

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