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BodhiAI
Nov. 9, 2019

Trignometric Ratios,Basic Identities,Sign Of Trignometric Ratio in Different Quardrants:

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Trigonometric Angles and Basic Formulae 

The functions sin, cos, tan, cosec, sec, cot are called circular functions or trigonometric functions.

a) or

b) or

c) or

d)

e)

or

f)

or

Important

It should be noted that sin does not mean product of sin and rather sin implies sine of angle .

Domain And Range of Trigonometrical Ratio(s)

T-Ratio

Domain (Of )

Range (of Function)

[-1, 1]

cos

R

[-1, 1]

tan where, cos 0

R

R

where,

R=

R

where,

R

R

 














Signs of Trigonometrical Ratio(s)

Let P(x, y) be any point in the rectangular plane represented by X'OX and Y'OY axes. If the line OP revolves in this plane starting from its initial position OX, then in any position of the revolving line the angle which it makes with OX is taken with +iv and -iv sign according as it is measured in anticlockwise or clockwise direction. Thereby, four cases arise

Case A: I Quadrant

x > 0, y > 0. Also,

Since, sin

Also,

and tan

I Quadrant

All T-Ratios are +iv in I-Quadrant 

Case B: II Quadrant

x < 0, y > 0. Also,

Since,

Also,

and

II Quadrant

sin and cosec are Positive

But, cos, tan, sec, cot are Negative

Case C: III Quadrant 

x < 0, y < 0. Also,

Since,

Also,

and

III Quadrant 

tan and cot are Positive

But, sin, cos, cosec, sec are Negative 

Case D: IV Quadrant 

x > 0, y < 0. Also,

Since,

Also,

and

IV Quadrant

cos and sec are Positive

But, sin, tan, cosec and cot are Negative

Problem Solving Trick 

The above Rules of Thumb can be remembered by remembering 

Quadrant I II III IV

All Since Tan Cos

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