PPT: Trigonometry | Quantitative Aptitude (Quant) - CAT PDF Download

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Trigonometry
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Trigonometry
What is Trigonometry?
1
Definition
Trigonometry studies 
relationships between 
sides and angles of 
triangles. The term comes 
from Greek words 
'Trigonon' (three angles) 
and 'metron' (measure).
2
Trigonometric Ratios
Ratios between sides of a 
right-angled triangle are 
called trigonometric ratios 
or functions. The six main 
ratios are: sine, cosine, 
tangent, cosecant, secant, 
and cotangent.
3
Right-Angled Triangle
In a right-angled triangle ABC, the longest side is the 
hypotenuse, while the other two sides are referred to as 
adjacent and opposite sides.
Page 3


Trigonometry
What is Trigonometry?
1
Definition
Trigonometry studies 
relationships between 
sides and angles of 
triangles. The term comes 
from Greek words 
'Trigonon' (three angles) 
and 'metron' (measure).
2
Trigonometric Ratios
Ratios between sides of a 
right-angled triangle are 
called trigonometric ratios 
or functions. The six main 
ratios are: sine, cosine, 
tangent, cosecant, secant, 
and cotangent.
3
Right-Angled Triangle
In a right-angled triangle ABC, the longest side is the 
hypotenuse, while the other two sides are referred to as 
adjacent and opposite sides.
Trigonometric Ratios of Right-Angled 
Triangle
Sine (sin)
Sine of an angle is defined as 
the ratio of the perpendicular 
to the hypotenuse.
Sin » = 
Perpendicular/Hypotenuse
Alternatively: » = sin-1 (P/H)
Cosine (cos)
Cosine of an angle is defined as 
the ratio of the base to the 
hypotenuse.
Cos » = Base/Hypotenuse
Alternatively: » = cos-1 
(Base/Hypotenuse)
Tangent (tan)
T angent of an angle is defined 
as the ratio of the 
perpendicular to the base.
T an » = Perpendicular/Base
Alternatively: » = tan-1 
(Perpendicular/Base)
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Trigonometry
What is Trigonometry?
1
Definition
Trigonometry studies 
relationships between 
sides and angles of 
triangles. The term comes 
from Greek words 
'Trigonon' (three angles) 
and 'metron' (measure).
2
Trigonometric Ratios
Ratios between sides of a 
right-angled triangle are 
called trigonometric ratios 
or functions. The six main 
ratios are: sine, cosine, 
tangent, cosecant, secant, 
and cotangent.
3
Right-Angled Triangle
In a right-angled triangle ABC, the longest side is the 
hypotenuse, while the other two sides are referred to as 
adjacent and opposite sides.
Trigonometric Ratios of Right-Angled 
Triangle
Sine (sin)
Sine of an angle is defined as 
the ratio of the perpendicular 
to the hypotenuse.
Sin » = 
Perpendicular/Hypotenuse
Alternatively: » = sin-1 (P/H)
Cosine (cos)
Cosine of an angle is defined as 
the ratio of the base to the 
hypotenuse.
Cos » = Base/Hypotenuse
Alternatively: » = cos-1 
(Base/Hypotenuse)
Tangent (tan)
T angent of an angle is defined 
as the ratio of the 
perpendicular to the base.
T an » = Perpendicular/Base
Alternatively: » = tan-1 
(Perpendicular/Base)
Trigonometric Ratios of 
Specific Angles
Angle 
»
0° 30° 45° 60° 90°
sin » 0 1/2 1/:2 :3/2 1
cos » 1 :3/2 1/:2 1/2 0
tan » 0 1/:3 1 :3 >
The trigonometric ratios of some special angles (0° , 30° , 45° , 
60° , 90°) follow a pattern and are easy to remember. Identifying 
and remembering these patterns helps in solving problems 
involving these angles.
Two angles are said to be complementary if their sum is 90° . 
Thus » and (90° 3 ») are complementary angles. Representing 
complementary angles in terms of standard angles helps in 
solving complex problems.
Page 5


Trigonometry
What is Trigonometry?
1
Definition
Trigonometry studies 
relationships between 
sides and angles of 
triangles. The term comes 
from Greek words 
'Trigonon' (three angles) 
and 'metron' (measure).
2
Trigonometric Ratios
Ratios between sides of a 
right-angled triangle are 
called trigonometric ratios 
or functions. The six main 
ratios are: sine, cosine, 
tangent, cosecant, secant, 
and cotangent.
3
Right-Angled Triangle
In a right-angled triangle ABC, the longest side is the 
hypotenuse, while the other two sides are referred to as 
adjacent and opposite sides.
Trigonometric Ratios of Right-Angled 
Triangle
Sine (sin)
Sine of an angle is defined as 
the ratio of the perpendicular 
to the hypotenuse.
Sin » = 
Perpendicular/Hypotenuse
Alternatively: » = sin-1 (P/H)
Cosine (cos)
Cosine of an angle is defined as 
the ratio of the base to the 
hypotenuse.
Cos » = Base/Hypotenuse
Alternatively: » = cos-1 
(Base/Hypotenuse)
Tangent (tan)
T angent of an angle is defined 
as the ratio of the 
perpendicular to the base.
T an » = Perpendicular/Base
Alternatively: » = tan-1 
(Perpendicular/Base)
Trigonometric Ratios of 
Specific Angles
Angle 
»
0° 30° 45° 60° 90°
sin » 0 1/2 1/:2 :3/2 1
cos » 1 :3/2 1/:2 1/2 0
tan » 0 1/:3 1 :3 >
The trigonometric ratios of some special angles (0° , 30° , 45° , 
60° , 90°) follow a pattern and are easy to remember. Identifying 
and remembering these patterns helps in solving problems 
involving these angles.
Two angles are said to be complementary if their sum is 90° . 
Thus » and (90° 3 ») are complementary angles. Representing 
complementary angles in terms of standard angles helps in 
solving complex problems.
Trigonometric Ratios of Complementary Angles
Sine & Cosine
sin(90° 3 A) = cos A
cos(90° 3 A) = sin A
Tangent & Cotangent
tan(90° 3 A) = cot A
cot(90° 3 A) = tan A
Secant & Cosecant
sec(90° 3 A) = cosec A
cosec(90° 3 A) = sec A
Basic Trigonometric Identities
sin² » + cos² » = 1
tan² » + 1 = sec² »
cot² » + 1 = cosec² »
sin »/cos » = tan »
cos »/sin » = cot »