We have facilitated this service for students of Grades 1 - 12 covering all major subjects*.
INVITE YOUR FRIENDS & Experience the New-Age of Learning from the Safety of your Home
Visit https://vdnt.in/COVID for MORE
➔ 4000+ hours of LIVE online teaching
➔ 40+ Teachers; from Top IITs and 10+ years experience
➔ 750 Tests & 3000 Assignments for Practical Application
➔ Instant Doubt Solving By Academic Mentors
➔ Replay/Recording of Classes If You’ve Missed
➔ Rank Booster Quizzes
➔ Previous Paper Analysis
Vedantu JEE 2022 Program- F E A T U R E S -
Boost your learning with Vedantu Pro
Enroll for FREEvdnt.in/YTJEE22
TRIGONOMETRY - LESSON 1
sinθ
cosθ
tanθ
00
0
1
0
12
1√2
2√3 1
√21
√31
300 450
12
√3
0
Undefined
900
2√3
600
1
0π6
π4
π3
π2T-ratio
Angle (θ)
Trigonometric functions of particular angles
TRIGONOMETRY - LESSON 1
TRIGONOMETRIC IDENTITIES
1. sin2θ + cos2θ = 1
2. sec2θ – tan2θ = 1
3. cosec2θ – cot2θ = 1
TRIGONOMETRY - LESSON 1
If sinθ + sin2θ = 1 Prove that 1+ =cos12θ 3 cos10 θ+ +3cos8 θ cos6 θExample: 2
TRIGONOMETRY - LESSON 1
If sinθ + sin2θ = 1 Prove that 1+ =cos12θ 3 cos10 θ+ +3cos8 θ cos6 θExample: 2
TRIGONOMETRY - LESSON 1
Eg 3. If x = secθ - tanθ, y = cosecθ + cotθ, then xy + 1 = ……...
A
B
D
C
x + y
x - y
y - x
-x - y
TRIGONOMETRY - LESSON 1
Q.If x = secθ - tanθ, y = cosecθ + cotθ, then xy + 1 = ……...
A
B
D
C
x + y
x - y
y - x
-x - y
TRIGONOMETRY - LESSON 1
Definition
Measurement of an Angle
1. Sexagesimal system (British System)
It is denoted by 10
If the central angle is divided into 360 equalparts, each part in it is called One degree.
Definition
Again if 10 is divided into 60 equal parts each part in it called One minute.
It is denoted as 1′. 10 = 60′
&
y′
x′ x
y
O
TRIGONOMETRY - LESSON 1
Definition
It is denoted as 1′′
If each 1′ is subdivided into 60 equal parts eachpart in it is called One second.
1′ = 60′′
Measurement of an Angle
1. Sexagesimal system (British System)
TRIGONOMETRY - LESSON 1
Definition
One radian is denoted as 1c.
A radian is an angle subtended at the centre ofa circle by an arc
r
B
A
r
r1c
whose length is equal to the radius of the circle.
Measurement of an Angle
2. Circular system (or) Radian Measure
Definition
Angle subtended at the centre of a circle of radius r by an arc of length l is defined as θ = l/r radians.
TRIGONOMETRY - LESSON 1
Relation between radians and degrees
∴ 1c =1800
π
1c ≈ (57.272…)0
3600 = 2πc
1c =(180)0
22
7
=0
11
630Clearly 1c • 10
90
11
Remember
➢ To convert radians into degree multiply with
➢ To convert degrees into radians multiply with
π1800
1800
π
TRIGONOMETRY - LESSON 1
Express the following angles in degrees.
i)5π12
c
=
ii)7π12
c
–
iii)13
c
=
=
Example:1
TRIGONOMETRY - LESSON 1
i
Express the following angles in degrees.
i)5π12
c
= 750
ii)7π12
c
– 105 0–
iii)13
c
=
=
60π
0
Example:1
Answer
iv) 11/16
TRIGONOMETRY - LESSON 1
=
Express the following angles in radians.
i) 1200
=ii) 6000–
=iii) 1440–
Example
TRIGONOMETRY - LESSON 1
=
Express the following angles in radians.
i) 1200
=ii) 6000–
2π c
3
=iii) 1440–
–10π 3
c
4πc 5
–
Example: 2
Answer
➔ 45 Live Classes By Best Teachers○ 3 sessions everyday - Mon to Sat
➔ 35 Comprehensive Tests; Assignments & Detailed Analysis
➔ Doubt Solving By Academic Mentors
➔ Replay/Recording of Classes If You’ve Missed
➔ Important Tips & Tricks To Crack JEE
➔ Rank Booster Quizzes
➔ Previous Paper Analysis
JEE Mains Crash Course- F E A T U R E S -
differential equations class 12 iit jee
➔ 90 Live Classes By Best Teachers○ 3 sessions everyday - Mon to Sat for 6 weeks
➔ 20+ Comprehensive Tests; Assignments & Detailed Analysis
➔ Unlimited Doubt Solving inside & outside class
➔ Replay/Recording of Classes If You’ve Missed
➔ Important Tips & Tricks To Crack JEE
➔ In class Rank Booster Quizzes
➔ Previous Paper Analysis
JEE Mains 2020 Crash Course- F E A T U R E S -
JEECrash Course
Lightning Deal: ₹ 24999 ₹ 5999
Use Coupon Code: NAGCCBuy Now @ https://vdnt.in/JEECCE
Step-1:Click on “ENROLL NOW”
Step -2:Click on “I have a coupon code”
Step-3:Apply Coupon NAGCC
How to Avail The Lightning Deal
Visit the link mentioned below
https://vdnt.in/JEECCE
TRIGONOMETRY - LESSON 1
Example:3 A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight and describes 88m when it has traced out 720 at the center, find the length of the rope.
TRIGONOMETRY - LESSON 1
Ar720
P
B
A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight and describes 88m when it has traced out 720 at the center, find the length of the rope.
B
A
Example: 3
Answer
=length of the rope 70 meters
TRIGONOMETRY - LESSON 1
Let P be a point on the circle such that OP makes angle θ with the x axis in Anticlockwise direction i.e. ∠AOP = θ
Consider a unit circle (i.e. the circle with radius = 1) with centre at the origin O.
O 1
y′
xA
Then cosθ and sin θare defined ascosθ = x – coordinate of Psin θ = y – coordinate of P
y′
x′ x
y
O 1
P(cos θ, sin θ)
θ
TRIGONOMETRY - LESSON 1
Remark
1. θ is positive in anticlockwise direction.
2. θ is negative in clockwise direction.
3. cosθ and sinθ are defined for all θ∈R. ( R : set of all real numbers)
x
y
θ
P(x , y)
OA(1,0)(-1,0)A’
B(0,1)
B’(0,-1)
-θ
4. -1≤ cosθ ≤ 1 -1 ≤ sin θ ≤ 1 for all θ∈R. ( R : set of all real numbers)
TRIGONOMETRY - LESSON 1
Sign of Trigonometric Functions
cosθ < 0 ; sinθ < 0
cosθ < 0 ; sinθ > 0 cosθ > 0 ; sinθ > 0
cosθ > 0 ; sinθ < 0
III
III IV
x
y
x > 0, y > 0x < 0, y > 0
x < 0, y < 0 x > 0, y < 0
TRIGONOMETRY - LESSON 1
y′
x′ x
y
O 1
P(cos θ, sin θ)
θ θ + 2π
P(cos (θ+ 2π), sin (θ+ 2π))
cosθ = cos (θ + 2π) = cos(θ + 4π)= …sinθ = sin (θ + 2π) = sin(θ + 4π)= …
In general
TRIGONOMETRY - LESSON 1
Other trigonometric ratios
1. tan θ = sin θ
cos θ π2
θ ≠ odd multiple of 2. sec θ =
1
cos θ
3. cot θ = cos θ
sin θ π,θ ≠ any multiple of 4. cosec θ =
1
sin θ
TRIGONOMETRY - LESSON 1
T-ratio
Angle (θ)
sinθ
cosθ
tanθ
900
(0, 1)
Not defined
1800 2700
0
3600
π 3π2
2π
Trigonometric functions of particular angles
π2
0
X′
Y
900
(cosθ, sinθ)
0
1 (–1, 0)
–1
0
(0, –1)0
–1
(1, 0)
1
0
1800
2700
3600
Not defined