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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
Formulas are extremely essential when solving questions in trigonometry in
competitive exams like SSC CGL. This is the 2

^{nd}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.

Let
us assume an angle of θ

_{1}lying in the 1^{st}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 0*^{0 }-^{ }90^{0})

*In Quadrant 2 all trigonometric ratios of sinθ and cosecθ are positive. (angles between 90*^{0 }-^{ }180^{0})

*In Quadrant 3 all trigonometric ratios of cosθ and secθ are positive. (angles between 180*^{0 }-^{ }270^{0})

*In Quadrant 4 all trigonometric ratios of tanθ and cotθ are positive. (angles between 270*^{0 }-^{ }360^{0})

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-

We need to understand that trigonometric
ratios would change for angles-

and they will remain same for 180

^{0}__+__θ and for 360^{0}__+__θ.
Let’s see what happens when we add or
subtract θ from 90

^{0}or 270^{0}-
This is because any angle that is 270

^{0}+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. 270^{0}-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 180

^{0}__+__θ and for 360^{0}__+__θ, the signs will remain the same.
For 360

^{0}+θ, the angle will complete one full rotation and then lie in quadrant 1 where all trigonometric ratios are positive.
So there are 2 important things to
remember-

1. The sign of the trigonometric ratios change
based on the value of θ.

2. sin becomes cos and cos becomes sin for 90

^{0}__+__θ and for 270^{0}__+__θ and it remains the same for 180^{0}__+__θ and for 360^{0}__+__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.

The
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**

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

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

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**Trigonometry Formulas: Values of Trigonometric Ratios**

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

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