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**Trigonometry Formulas are extremely handy to solve questions in**

trigonometry. Most of trigonometry formulas play around with trigonometric

ratios. Read on for a complete list of Trigonometry Formulas.

trigonometry. Most of trigonometry formulas play around with trigonometric

ratios. Read on for a complete list of Trigonometry Formulas.

Trigonometry

Formulas are extremely essential when solving questions in trigonometry in

competitive exams like SSC CGL. This is the 2nd blog in our series on

Trigonometry where you will get a complete list of trigonometry formulas that

form the basics of solving questions in trigonometry. In the 1st blog of the

series we discussed- what is trigonometry and the different trigonometric

ratios. Taking that a step ahead we will now discuss trigonometric formulas

relating the ratios. Before that you must go through the basics of

trigonometry.

Formulas are extremely essential when solving questions in trigonometry in

competitive exams like SSC CGL. This is the 2nd blog in our series on

Trigonometry where you will get a complete list of trigonometry formulas that

form the basics of solving questions in trigonometry. In the 1st blog of the

series we discussed- what is trigonometry and the different trigonometric

ratios. Taking that a step ahead we will now discuss trigonometric formulas

relating the ratios. Before that you must go through the basics of

trigonometry.

###
**Signs of Trigonometric Ratios**

A

lot of trigonometry formulas are based on the signs of trigonometric ratios,

based on the quadrants they lie in. Therefore it becomes extremely essential

for us to understand how trigonometric ratios get the positive or negative

sign. The sign is based on the quadrant in which the angle lies.

lot of trigonometry formulas are based on the signs of trigonometric ratios,

based on the quadrants they lie in. Therefore it becomes extremely essential

for us to understand how trigonometric ratios get the positive or negative

sign. The sign is based on the quadrant in which the angle lies.

Let

us assume an angle of θ1

lying in the 1st quadrant and an angle θ in quadrant one and two combined.

So let us see how signs change with respect to the quadrant they lie in.

us assume an angle of θ1

lying in the 1st quadrant and an angle θ in quadrant one and two combined.

So let us see how signs change with respect to the quadrant they lie in.

*In Quadrant 1 all trigonometric ratios*

are positive. (angles between 00 – 900)are positive. (angles between 00 – 900)

*In Quadrant 2 all trigonometric ratios*

of sinθ and cosecθ are positive. (angles between 900 – 1800)of sinθ and cosecθ are positive. (angles between 900 – 1800)

*In Quadrant 3 all trigonometric ratios*

of cosθ and secθ are positive. (angles between 1800 – 2700)of cosθ and secθ are positive. (angles between 1800 – 2700)

*In Quadrant 4 all trigonometric ratios*

of tanθ and cotθ are positive. (angles between 2700 – 3600)of tanθ and cotθ are positive. (angles between 2700 – 3600)

θ is the angle made between the x-axis and the

line, in the anti-clockwise direction. If we move in the clockwise direction,

the angle will be taken as – θ. We know

that in quadrant 4, only cosθ and secθ will be positive, the others will be

negative, therefore-

line, in the anti-clockwise direction. If we move in the clockwise direction,

the angle will be taken as – θ. We know

that in quadrant 4, only cosθ and secθ will be positive, the others will be

negative, therefore-

We need to understand that trigonometric

ratios would change for angles-

ratios would change for angles-

and they will remain same for 1800

and for 3600

__+__θand for 3600

__+__θ.
Let’s see what happens when we add or

subtract θ from 900 or 2700-

subtract θ from 900 or 2700-

This is because any angle that is 2700+θ

will fall in quadrant 4 and in this quadrant only trigonometric ratios of cos

and sec are positive. So the above will be negative. 2700-θ will

fall in the quadrant 3 and in this quadrant trigonometric ratios of tan and cot

are positive, so it will again be negative.

will fall in quadrant 4 and in this quadrant only trigonometric ratios of cos

and sec are positive. So the above will be negative. 2700-θ will

fall in the quadrant 3 and in this quadrant trigonometric ratios of tan and cot

are positive, so it will again be negative.

For 1800

3600

__+__θ and for3600

__+__θ, the signs will remain the same.
For 3600+θ, the angle will

complete one full rotation and then lie in quadrant 1 where all trigonometric

ratios are positive.

complete one full rotation and then lie in quadrant 1 where all trigonometric

ratios are positive.

So there are 2 important things to

remember-

remember-

1. The sign of the trigonometric ratios change

based on the value of θ.

based on the value of θ.

2. sin becomes cos and cos becomes sin for 900

and for 2700

and for 3600

__+__θand for 2700

__+__θ and it remains the same for 1800__+__θand for 3600

__+__θ.###
**Trigonometry Formulas: Trigonometric Identities**

After

looking at the trigonometric ratios, let us move on to trigonometric identities,

which are the basics of most trigonometry formulas.

looking at the trigonometric ratios, let us move on to trigonometric identities,

which are the basics of most trigonometry formulas.

The

above identities hold true for any value of θ.

above identities hold true for any value of θ.

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**Trigonometry Formulas: Sum and Difference of Angles**

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**Trigonometry Formulas: Double Angle Formulas**

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**Trigonometry Formulas: Triple Angle Formulas**

###
**Trigonometry Formulas: Converting Product into Sum and Difference**

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**Trigonometry Formulas: Converting Sum and Difference into Product**

###
**Trigonometry Formulas: Values of Trigonometric Ratios**

These

formulas are required to solve trigonometry questions in the traditional way.

formulas are required to solve trigonometry questions in the traditional way.

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