Trigonometric ratios of 90+theta,90-theta,180+theta etc

Let us understand the trigonometric ratios of (90+θ),(90-θ),(180+θ),(180-θ)etc. In addition I have provided all these ratios in a single picture.

In the previous posts, we have learned the signs of trigonometric ratios in various quadrants.[Signs of trigonometric functions in various quadrants]

NOTE  that, the trigonometric ratios changes in (2n+1)\frac { \pi }{ 2 } ±θ i.e

  • sin changes to cos or vice versa
  • cosec changes to sec or vice versa
  • tan changes to cot or vice versa

For example, sin (90+θ)=cosθ

and cos(90+θ)=-sinθ

 It is equally important to know that the signs of the trigonometric ratios will depend upon the quadrants.

Also, there is no change in the trigonometric ratios in (nπ±θ)

Another example, sin(180+θ)=-cosθ and sec (360-θ)=secθ

Recalling the signs of trigonometric ratios in various quadrants-

 All trigonometric functions in the first quadrant are positive. 

 In 2nd quadrant only sin and cosec are positive. 

  Under the 3rd quadrant only tan and cot are positive. 

  In the fourth quadrant only cos and sec are positive. 


With this in mind have a look at the image below.


trigonometric ratios 90+theta,90-theta.180+theta

This image will be beneficial for finding trigonometric ratios of 90+θ,90-θ,180+θ etc.

You can also visit the page where I have provided all trigonometric formulas.

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