How to Memorize the Relationships between Trigonometry Functions Square Relationships

 

The square relationships in trigonometry functions are often tested in trigonometry exams and extensively used in single variable calculus. So today I will show you how to memorize them effectively.

 

First of all, draw a hexagon as follows. Remember, sine (sin) and cosecant (csc) is in reciprocal relationship, so they are on opposite sides of the hexagon. Similarly, cosine (cos) is on the opposite side of secant (sec), tangent (tan) is on the opposite side of cotangent (cot). Then put squares on all of them.

                                                                   

By the way, this arrangement is fixed, sine and cosine have to be one top, tangent and cotangent in the middle, then secant and cosecant must be at the button, otherwise this will not work!

Then as what is shown along with the arrows, you can discover the following relationships:

sin²X+cos²X=1

tan²X+1=sec²X

1+cot²X=csc²X

Easy right? So now you can remember them easily and have more time to focus on other things important on trigonometry and calculus!

(This is important when doing derivatives in calculus as well.)