Question

what is the basic concept of trigonometry?

Answer 1

★★★ TRIGONOMETRY ★★★

➡ Trigonometry :-
Trigo + metry
The measurement of side lengths, angles , and many properties of traingles is known as trigonometry.

➡ Actually Trigonometry is very big branch of mathematics , but some basic term help to understand whole concept of it .

::::(1):::
★★ Measurement of angles ★★

1) sexagesimal system :-
in this system, angle is measured in degree , minutes and second . A complete rotation describes 360° .

1 right angle = 90°
1° = 60' ( 60 minutes )
1' = 60" ( 60 second )


2) centesimal or French system :-
in this system , angle is measured in grade , minutes and second.
1 right angle = 100^g ( 100 grade)
1^g = 100' ( 100 minutes )
1' = 100" ( 100 second)


3) circular system :-
in circular system , unit of measurement is RADIAN . one radian written as 1^c ,
the measure of angle subtended at the radius of a circle by an arc of length of equal to the radius of the circle .
(i) π radian = 180°
(ii) 1 radian = π/180°


::::::::::::(2):::::::::::;;;;;;

TRIGONOMETRICAL ratio & identies .
————————————————
in ABC , right angle ∆
right angled at B , there are six possible ratio is named as follows :

↔sin∅ = Perpendicular (P)/Hypotenuse (H)
↔cos∅ = base ( B)/Hypotenuse
↔ tan∅ = perpendicular (P)/Hypotenuse ( H)
↔cosec∅ = H/P
↔sec∅ = H/B
↔ cot∅ = B/P



★ <> -1 ≤ sin∅ ≤ 1 { means value of sin∅ lies between -1 to 1 . }
<> -1 ≤ cos∅ ≤ 1

<> -∞ < tan∅ < ∞ { means value of tan∅ is possible any real number }
<> -∞ < cot < ∞

<> sec∅ ≤ -1 , sec∅ ≥ 1 { means value of sec∅ always less then -1 or greater then, 1 . it's value never possible in -1 to 1 }
<> cosec∅ ≤ -1 , cosec∅ ≥ 1


★ In co- ordinate axes //
<>1st - Quadrant => all ratios will be positive
<>2nd - Quadrant => sin∅, cosec∅ are positive and rest negative.
<> 3rd - Quadrant => tan∅ , cot∅ are positve and rest negative
<> 4th -Quadrant => cos∅, sec∅ are positive and rest are negative .

★ sin( 90° ± ∅) = cos∅
sin( 180°- ∅) = sin∅
sin( 180° + ∅) = - sin∅
sin( 270° ± ∅) = - cos∅
sin( 360+∅) = sin∅
sin( 360- ∅) = - sin∅

[ you can find out ratios in all quadrant by using above co-ordinate axes concept . I gave here only sample .]

★ Some important identies of Trigonometry.
—————————————————
<> sin²∅ + cos²∅ = 1
<> sec²∅ - tan²∅ = 1
<> cosec²∅ - cot²∅ = 1
<> tan∅ = sin∅/cos∅
<> sin( -x) = -sinx : cosec(-x) = -cosecx
<> tan(-x) = -tanx ; cot(-x) = -cotx
<> cos( -x) = cosx ; sec(-x ) = - secx


★★some useful property for finding value of ratios in 15°, 75°, 18° , 72°, 22½° etc.★★

<> sin( A ±B) = sinA.cosB ± cosA.sinB
<> cos(A -B) = cosA.cosB+ sinA.sinB
<> cos( A + B) = cosA.cosB - sinA.sinB
<>tan( A + B) = ( tanA+ tanB)/(1-tanA.tanB)
<>tan(A - B)= (tanB - tanB)/( 1 - tanA.tanB)

[ note :- Here I gave only some terms . I hope this help you . but this is not enough . you should read book and your sir assignment if you go to class or coaching ]

Answer 2

* Many geomtric concepts helps us in

solving problems we come across in

our daily life in various situations.

We may know the properties of

similar triangles and theorems

regarding them formally, but they

may not helpful in connecting the

ratios of sides in a triangle with its

angles.

When we proceed to define these

relationships many problems in

mathematics are facilitated to solve.

This procedure was in use during

500BC.Different astronomical

calculations were done by using this

procedure.

* The word " trigonometry" is derived

from the Geeek word " Tri " means

"Three ",

"Gonia" means " an angle " and

" metron " means " Measure".

Hilparachus is considered as " Father

of Trigonometry."

Basic concepts of Trigonometry:
__________________________

1. Relation among degrees , grades

and radians:

D/ 90 = G / 100 = 2C / pi

Using this relation we can convert

one system to another system easily.

2) Trigonometric ratios of an angle:

i ) sin A
= ( length of the side opposite
to angle A )/ length of hypotenuse

ii ) cos A
= ( length of the side adjacent to an angle A )/ length of hypotenuse

iii) tan A = ( length of the side opposite to angle A )/ ( length of the side adjacent to angle A )

Relations :
_________
i . sin A cosec A = 1 or
sin A = 1/ cosecA

ii) cos A secA = 1

iii) tanA cotA =1

Identities:
_________

An identity equation having trigonometric ratios of an angle is called trigonometric identity and is true for all values of the angles invovled in it.

1) sin ^2 A + cos ^2 A = 1

i ) sin^2 A = 1 - cos ^2 A

ii) cos ^2 A = 1 - sin ^2 A

2) 1 + tan ^2 A = sec ^2 A

i ) sec^2 A - tan ^2 A = 1

( sec A + tan A ) ( sec A - tan A ) = 1

3) 1 + cot ^2 A = cosec ^2 A

********
-> Signs of the Trigonometric ratios:
Note : With " All Silver Tea Cups "

we can remember the signs of trigonometric ratios.

******

Trigonometry is widely used in life around us. Trigonometry used in all most all fields in our daily life.
The knowledge of Trigonometry is used to construct maps to calculate the distances from earth to the planets and stars ., etc.
In tenth class we used it in finding heights and distances of various objects , without actually measuring them.

Here we learn the concepts:
1) Line of sight

2) Angle of elevation

3) Angle of depression.

You can combine the Abhi and my explanation it will be more beneficial to you.

I hope this will usful to you.

****