Made by:BHAVUN CHHABRA 10TH - B

Trigonometry is the study and solution of Triangles. Solving a triangle means finding the value of each of its sides

and angles. The following terminology and tactics will be important in the

solving of triangles.Pythagorean Theorem (a2+b2=c2). Only for right angle triangles

Sine (sin), Cosecant (csc or sin-1)

Cosine (cos), Secant (sec or cos-1)

Tangent (tan), Cotangent (cot or tan-1)

Right/Oblique triangle

Since a triangle has three sides, there are six ways to divide the lengths of the sides

Each of these six ratios has a name (and an abbreviation)

Three ratios are most used: sine = sin = opp / hyp cosine = cos = adj / hyp tangent = tan = opp / adj

The other three ratios are cosecant= cosec= hyp/

opp secant= sec= hyp/ adj cotangent = cot = adj/opp

The ratios depend on the shape of the triangle (the angles) but not on the size

hypotenuse

adjacent

op

posi

tehypotenuse

adjacentopposi

te

OPPO

SITE SIDE

angle

angle

angle

opposit

e

opposite

opposit

e

oppositeangle

THE SIDE OPPOSITE TO THE ANGLE

adjacent

adjacen

t

adjacen

t

angle

angle

angle

angle

AD

JAC

EN

T

THE SIDE ADJACENT TO THE ANGLE

hypote

nuse

hypote

nuse

hypotenuse

hypotenuse

HYPO

TENUSE

THE LONGEST SIDE

There are 3 kinds of trigonometric ratios we will learn.

sine ratio

cosine ratio

tangent ratio

THREE TYPES TRIGONOMETRIC THREE TYPES TRIGONOMETRIC RATIOSRATIOS

For any right-angled triangle

Sin = Opposite side

hypotenuses

sine ratio

For any right-angled triangle

Cos =

hypotenuses

Adjacent Side

For any right-angled triangle

tan = Adjacent Side

Opposite Side

Reciprocal Identities

Quotient Identities

Pythagorean Identities

Negative-Number Identities

sin1

csccos

1sec

tan1

cot

sincos

cotcossin

tan

222222 csccot1sec1tan1cossin

tan)tan(cos)cos(sin)sin(

Work with one side at a time. We want both sides to be exactly the

same. Start with either side Use algebraic manipulations and/or the

basic trigonometric identities until you have the same expression as on the other side.

xxx cossincot

x

xx

x

xx

cos

sinsin

cos

sincot LHS

and xcos RHS

Since both sides are the same, the identity is verified.

Change everything on both sides tosine and cosine.

Start with the more complicated side Try substituting basic identities (changing all

functions to be in terms of sine and cosine may make things easier)

Try algebra: factor, multiply, add, simplify, split up fractions

If you’re really stuck make sure to: