BodhiAI

Nov. 9, 2019
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)

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

After School To College

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