Trigonometry

Trigonometric Formulas

Trigonometry Formulas are extremely handy to solve questions in trigonometry. Most of trigonometry formulas play around with trigonometric ratios. 

Trigonometry Formulas are extremely essential when solving questions in trigonometry in competitive exams like SSC CGL. We are providing a complete list of trigonometry formulas that form the basics of solving questions in 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 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 0- 900)

In Quadrant 2 all trigonometric ratios of sinθ and cosecθ are positive. (angles between 90- 1800)

In Quadrant 3 all trigonometric ratios of cosθ and secθ are positive. (angles between 180- 2700)

In Quadrant 4 all trigonometric ratios of tanθ and cotθ are positive. (angles between 270- 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-

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

and they will remain same for 1800+θ and for 3600+θ.

Let’s see what happens when we add or 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.


For 1800+θ and for 3600+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.

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 900+θ and for 2700+θ and it remains the same for 1800+θ and 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.

The above identities hold true for any value of θ.

Trigonometry Formulas: Sum and Difference of Angles


Trigonometry Formulas: Double Angle Formulas


Trigonometry Formulas: Triple Angle Formulas


Trigonometry Formulas: Converting Product into Sum and Difference

Trigonometry Formulas: Converting Sum and Difference into Product

Trigonometry Formulas: Values of Trigonometric Ratios

 

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