Trignometry, Virk Jalanhdar

BALWINDER KUMAR (MATH MASTER) SURINDER KAUR (MATH MISTRESS) GOVT.SR.SEC.SCHOOL VIRK (JAL.)

. 1. To make the students familiar with term trigonometry , uses of it , basic formulas of it. 2. To create interest of students in it. 3. To make teaching of trigonometry effective.

What is Trigonometry It

is an important branch of mathematics . It is derived from to greek words *TRIGNON meaning triangle & *METRON meaning measurement.  Thus the word trigonometry means the

USES OF TRIGNOMETRY • Trigonometry helps us in calculating sides & angles of a triangle. • Surveying ,Geography ,Navigation Knowledge of trigonometry has been used extensively in Astronomy, ,Physical & Engineering Sciences etc.

• In right angled triangle ABC right angled at B • Let θ be the acute angle A in

right angled triangle. • Side AB opposite to angle θ is called perpendicular. • Side AC opposite to right angle is called hypotenuse. B • Remaining side BC is called base of triangle ABC.

Ө C

 In

right angled triangle ABC. h2=p2+b2 where h=hypotenuse p=perpendicular b=base

T- ratios OR Trignometric ratios  Some

ratios of differents sides of tringle are called T-ratios or trignometric ratios. E.g. Sin , Cos , Tan , Cosec , Sec , Cot.

Sin of an angle θ  The ratio of perpendicular/hypotenuse is

called the sin of an angle θ.  In short we can write it as Sinθ=AB/AC

A

Ө B

C

COS OF AN ANGLE θ 

 

The ratio of base/hypotenuse is called Cos of angle θ. A In short we can write it as Cos θ=BC/AC.

Ө B

C

TANGENT OF AN ANGLE θ  The

ratio of perpendicular/base is called Tan of angle θ. A  In short we can write it as Tan θ=AB/BC.

Ө B

C

Cosecant of an angle θ  The ratio of hypotenuse/perpendicular is

called the cosecant of an angle θ.  In short we can write it as Cosec θ=AC/AB

A

Ө B

C

SECANT OF AN ANGLE θ The ratio of hypotenuse/base is called Secant of angle θ.  In short we can write it asA Secθ=BC/AC. 

Ө B

C

COT OF AN ANGLE θ  The

ratio of base/perpendicular is called Cot of angle θ. A  In short we can write it as Cot θ=BC/AB.

Ө B

C

RELATION AMONG T-RATIOS 

Tanθ=Sinθ/Cosθ



Cosecθ=1/Sinθ



Secθ=1/Cosθ



Cotθ=1/Tanθ

POPULAR SONG TO LEARN • SA RE • PAN DI T • HAR

CHELE T ER E B ADRI PARS AD HAR BOLE In shor t we can wri tten as S C T P B P H H B

Si nθ=P/H Tan θ=P/B

Cos θ=B/h

T-RATIO OF SOME SPECIFIC ANGLES θ

0O

30O

45O

60O

90O

SINθ

0

1/2

1/√2

√3/2

1

COSθ

1

√3/2

1/√2

1/2

0

TANθ

0

1/√3

1

√3

∞

2

√2

2/√3

1

COSEC ∞ SECθ

1

2/√3

√2

2

∞

COTθ

∞

√3

1

1/√3

0

SOME TRIGNOMETRY RELATIONS      

SIN(- θ ) = - SINθ COS(- θ ) = COSθ TAN(- θ ) = - TANθ COSEC(- θ ) = - COSECθ SEC(- θ ) = SECθ COT(- θ ) = TANθ

SOME TRIGNOMETRIC FORMULE • SIN(90-θ) = COSθ • COS(90-θ) = SINθ • TAN(90-θ) = COTθ

SOME IMPORTANT FORMULE SIN2θ+COS2θ = 1 SIN2θ = 1- COS2θ COS2θ = 1- SIN2θ SEC2θ-TAN2θ = 1 SEC2θ = 1+TAN2θ TAN2θ = 1- SEC2θ SIN2θ = SINθ.COSθ

QUERY SESSION     

WHAT IS TRIGNOMETRY ? WHAT IS T-ROTIO ? WHAT IS TANGENT OF AN ANGLE ? WHAT IS SIN OF AN ANGLE ? WHAT IS COS OF AN ANGLE ?

BIBLIOGRAPHY  ALL

THE TRIGNOMETRIC RELATION AND FORMULE ARE SELECTED FROM BOOK OF CLASS 10th OF P.S.E.B.

ACKNOWLEDGEMENT We are very thankful to :-Principal .We are also very thankful to Miss Priya & Miss. Paramjit who provide us guidance & encourage us to achieve the goal of enhance education.