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CHAPTER
Introduction to
8 Trigonometry
KEY POINTS A
• A branch of mathematics which deals
with the problems related to right angled H (hypotenuse)
triangles. It is the study of relationship (Perpendicular) P
between the sides and angles of a right
angled triangel. C
Note : For ∠A — Perpendicular is BC B B
base is AB. (base)
For ∠C, Perpendicualr is AB Base is BC.
Trigonometric Rations of an acute angle in a right angled triangle express the
relationship between the angle and the length of its sides.
Sine
P
H Cosine
Tangent B
P H
B
Trigonometric
Ratios
Secant
Co-tangent H
B B
P Cosecant
H
P
Mind Trick: To learn the relationship of sine, cosine and tangent follow this
sentences.
Some People Have Curly Brown Hair Through Proper Brushing
P B P
sin A = cos A = tan A =
H H B
Mathematics-X 103
Source: EDUDEL
, 1. Trigonometric ratio : In ΔABC, ∠B = 90°. For ∠A,
C
Perpendicular Opposite side
sinA = =
Perpendicular
se
Hypotenuse Hypotenuse
eu
ten
po
Hy
Base adjacent side
cos A = =
Hypotenuse Hypotenuse
θ
B
Perpendicular Opposite side A Base
tan A = =
Base adjacent side
Base adjacent side
cot A = =
Perpendicular opposite side
Hypotenuse Hypotenuse
sec A = =
Base adjacent side
Hypotenuse Hypotenuse
cosec A = =
Perpendicular Opposite side
2. Opposites
1 1
sin θ = , cosec θ =
cosec θ sin θ
1 1
cos θ = , sec θ =
sec θ cos θ
1 1
tan θ = , cot θ =
cot θ tan θ
sin θ cos θ
3. tan θ = , cot θ =
cos θ sin θ
4. Identities
sin2 θ + cos2 = 1 ⇒ sin2 θ = 1 – cos2 θ and cos2 θ = 1 – sin2 θ
1 + tan2 θ = sec2 θ ⇒ tan2 θ = sec2 θ – 1 and sec2 θ – tan2 θ = 1
1 + cot2 θ = cosec2 θ ⇒ cot2 θ = cosec2 θ – 1 and cosec2 θ – cot2 θ = 1
104 Mathematics-X
Source: EDUDEL
CHAPTER
Introduction to
8 Trigonometry
KEY POINTS A
• A branch of mathematics which deals
with the problems related to right angled H (hypotenuse)
triangles. It is the study of relationship (Perpendicular) P
between the sides and angles of a right
angled triangel. C
Note : For ∠A — Perpendicular is BC B B
base is AB. (base)
For ∠C, Perpendicualr is AB Base is BC.
Trigonometric Rations of an acute angle in a right angled triangle express the
relationship between the angle and the length of its sides.
Sine
P
H Cosine
Tangent B
P H
B
Trigonometric
Ratios
Secant
Co-tangent H
B B
P Cosecant
H
P
Mind Trick: To learn the relationship of sine, cosine and tangent follow this
sentences.
Some People Have Curly Brown Hair Through Proper Brushing
P B P
sin A = cos A = tan A =
H H B
Mathematics-X 103
Source: EDUDEL
, 1. Trigonometric ratio : In ΔABC, ∠B = 90°. For ∠A,
C
Perpendicular Opposite side
sinA = =
Perpendicular
se
Hypotenuse Hypotenuse
eu
ten
po
Hy
Base adjacent side
cos A = =
Hypotenuse Hypotenuse
θ
B
Perpendicular Opposite side A Base
tan A = =
Base adjacent side
Base adjacent side
cot A = =
Perpendicular opposite side
Hypotenuse Hypotenuse
sec A = =
Base adjacent side
Hypotenuse Hypotenuse
cosec A = =
Perpendicular Opposite side
2. Opposites
1 1
sin θ = , cosec θ =
cosec θ sin θ
1 1
cos θ = , sec θ =
sec θ cos θ
1 1
tan θ = , cot θ =
cot θ tan θ
sin θ cos θ
3. tan θ = , cot θ =
cos θ sin θ
4. Identities
sin2 θ + cos2 = 1 ⇒ sin2 θ = 1 – cos2 θ and cos2 θ = 1 – sin2 θ
1 + tan2 θ = sec2 θ ⇒ tan2 θ = sec2 θ – 1 and sec2 θ – tan2 θ = 1
1 + cot2 θ = cosec2 θ ⇒ cot2 θ = cosec2 θ – 1 and cosec2 θ – cot2 θ = 1
104 Mathematics-X
Source: EDUDEL
