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) R [-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

x > 0, y > 0. Also,

Since, sin

Also,

and tan

All T-Ratios are +iv in I-Quadrant

x < 0, y > 0. Also,

Since,

Also,

and

sin and cosec are Positive

But, cos, tan, sec, cot are Negative

x < 0, y < 0. Also,

Since,

Also,

and

tan and cot are Positive

But, sin, cos, cosec, sec are Negative

x > 0, y < 0. Also,

Since,

Also,

and

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

All Since Tan Cos

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