INTRODUCTION

Trigonometry is branch of mathematics. Which is derived from Greek Word

Tri threeGon sidesMetron measure

BASE (B)

HYPOTENUESE (H)

PERPEND I CULAR

(P)

T - RATIO`s

Sin θ = P/H = 1/Cosecθ

Cos θ = B/H = 1/Sec θ

Tan θ = P/B = Sin θ /Cos θ

Cosec θ = H/P = 1/Sin θ

Sec θ =H/B = 1/Cos θ

Cot θ = B/P = 1/Tan θ = Cos θ/Sin θ

θ

P

B

H

Funny Way To Learn T- Ratio`s

P B P Pandit Badri Prasad

H H B Har Har Bole

S C T Sona Chandi Tole

TRIGONOMETRIC - IDENTITIES•

2 2 1Sin Cos 2 21 tan sec 2 21 cot cosec

0° 30° 45° 60° 90°

Sin

Cos 1 0

Tan =

Cot =

Sec =

Cosec =

00

4

1 1

4 2 2 1

4 2 3 3

4 2

41

4

3

2

1

21

2

Sin

Cos

0

1

112

3 32

1

2 11

2

3

2 312

1

0

1

tan 3 1 1

3

0

1

cos

11

1 2

1

0

1

sin

1

0

22

1 2

1

2

31

11

√2√32

ANGLE OF ELEVATION – α , β (OBSERVER LOOK UPWARD)

βα

ANGLE OF DEPRESSION – α , β (OBSERVER LOOKING DOWNWARD)

β

α

α β

Measurement of Radian

Angle subtended at the centre by an arc of length 1 unit in a unit circle is said to have a measure of 1 radian.

1 Radian

1

1

O A

B

1

θ(r)

l

θ = l/r

l = r θ

Notational Convection

Radian measure π x Degree measure

Degree Measure

π x Radian measure

180 180

X

Y`

YFIRST QUADRANTSECOND QUADRANT

THIRD QUADRANT FOURTH QUADRANT

(ALL POSITIVE )(Sinθ ,Cosecθ Positive)

(90 - θ)(90 + θ)

(180 - θ)

(180 + θ)

(270 - θ)

(270 + θ)

(360 - θ)

X`

Sin (90 + θ) = Cosθ

Cos (90 + θ) = - Sinθ

(180 – θ) = Sinθ

Tan(90 + θ) = - Cotθ(180 – θ) = - Tanθ

(180 – θ) = - Cosθ

Sin(90 – θ) = CosθCos(90 – θ) = SinθTan(90 – θ) = CotθCot(90 – θ) = TanθSec(90 – θ) = CosecθCosec(90 – θ) = Secθ

Sin(180 + θ) = - Sinθ(270 – θ) = - Cosθ

Cos(180 + θ) = - Cosθ(270 – θ) = - Sinθ

Tan(180 + θ) = Tanθ(270 – θ) = Cotθ

Sin(270 + θ) = - Cosθ (360 - θ) = - Sinθ

Cos(270 + θ) = Sinθ(360 – θ) = Cosθ

Tan(270 + θ) = - Cotθ

(360 – θ) = - Tanθ

ADD

(Tanθ ,Cotθ Positive) (Cosθ ,Secθ Positive)

SUGAR

TO COFFEE

θ 0 Π

6

π

4

π 3

π2

4π

6

3π

4

5π

6

π 7π

6

5π

4

4π

3

3π

2

5π

3

7π

4

11π

6

2π

0 1

2

1

√2

√3

21 √3

2

1

√2

1

2

0 -1

2

-1

√2

-√3

2

-1 -√3

2

-1

√2

-1

2

0

0 π6

π 4

π 3

π2

4π6

3π4 5π6 π 7π6

5π4

4π3 3π2

5π3

7π4

11π 6

2ππ6π 4π 3

π2

4π6

3π4

5π6

π

1/2

1/√2√3/2

1

-1/2

-1/√2

-√3/2-1

Sinθ

θ 0 Π

6

π 4

π 3

Π

2

4π6

3π4

5π6

π 7π6

5π4

4π3

3π2

5π3

7π4

11π 6

2π

1 √3

2.

1

√2

1

2

0 -1

2

-1

√2

-√3

2

-1 -√3

2

-1

√2

-1

2

0 1

2

1

√2

√3

2

1

0 π6

π 4

π 3

π2

4π6

3π4 5π6 π 7π6

5π4

4π3 3π2

5π3

7π4

11π 6

2ππ6π 4π 3

π2

4π6

3π4

5π6

π

1/2

1/√2√3/2

1

-1/2

-1/√2

-√3/2-1

Cosθ

θ 0 Π

6

π 4

π 3

Π

2

4π6

3π4

5π6

π 7π6

5π4

4π3

3π2

5π3

7π4

11π 6

2π

0 1

√3

1 √3 ∞ -√3 -1 -1

√3

0 √3 1 √3 ∞ -√3 -1 -1

√3

0

0 π6

π 4

π 3

π2

4π6

3π4 5π6 π 7π6

5π4

4π3 3π2

5π3

7π4

11π 6

2ππ6π 4π 3

π2

4π6

3π4

5π6

π

1/2

1/√2√3/2

1

-1/2

-1/√2

-√3/2-1

Tanθ

θ 0 Π

6

π 4

π 3

Π

2

4π6

3π4

5π6

π 7π6

5π4

4π3

3π2

5π3

7π4

11π 6

2π

∞ √3 1 1

√3

0 -1

√3

-1 -√3 ∞ 1

√3

1 1

√3

0 -1

√3

-1 -√3 ∞

0 π6

π 4

π 3

π2

4π6

3π4 5π6 π 7π6

5π4

4π3 3π2

5π3

7π4

11π 6

2ππ6π 4π 3

π2

4π6

3π4

5π6

π

1/2

1/√2√3/2

1

-1/2

-1/√2

-√3/2-1

Cotθ

θ 0 Π

6

π 4

π 3

Π

2

4π6

3π4

5π6

π 7π6

5π4

4π3

3π2

5π3

7π4

11π 6

2π

1 2

√3

√2 2 ∞ -2 -√2 -2

√3

-1 -2

√3

-√2 -2 ∞ 2 √2 2

√3

1

0 π6

π 4

π 3

π2

4π6

3π4 5π6 π 7π6

5π4

4π3 3π2

5π3

7π4

11π 6

2ππ6π 4π 3

π2

4π6

3π4

5π6

π

1

-1

Secθ

2

2/√3

√2

-2/√3

-√2

-2

θ 0 π6

π 4

π 3

π2

4π

6

3π4

5π6

π 7π6

5π

4

4π3

3π2

5π3

7π4

11π 6

2π

∞ 2 √2 2

√3

1 2

√3

√2 2 ∞ -2 -√2 -2

√3

-1 -2

√3

-√2 -2 ∞

0 π6

π 4

π 3

π2

4π6

3π4 5π6 π 7π6

5π4

4π3 3π2

5π3

7π4

11π 6

2ππ6π 4π 3

π2

4π6

3π4

5π6

π

1

2/√3√2

2

-1

-√2

-2/√3

-2

Cose

cθ