TRIGONOMETRY #1(REASON BEHIND THE QUADRANT SIGN)

WHY THE QUADRANT HAVE ASSIGNED SIGN IN CARTESIAN PLANE?

Lets Think why the quadrant have assigned fixed value as follows::

1st Quadrant = sin,cos,tan,cot,cosec,sec (ALL ARE POSITIVE HERE )

2nd Quadrant= Only sin,cos (POSITIVE)

3rd Quadrant= Only tan.cot(POSITIVE)

4th Quadrant=Only cos,sec (POSITIVE)

##NOTE::REST ALL ARE NEGATIVE IN THEIR RESPECTIVE QUADRANT

TRY TO VISUALIZE WHY THIS HAPPENS LIKE THIS??WHAT IS  THE REASON BEHIND THAT (THINK AT LEAST 15-20mins)

THEN LOOK FOR THE SOLUTION:: :)

:::::::::::::::::::::::::::::::::::::::::::::SOLUTION::::::::::::::::::::::::::::::::::::::::::::::::

FIRST OF ALL KNOW THIS  NEW DEFINATION  OF ALL TRIGONOMETRY RATIO 

SINθ= Y coordinate/Hypotenuse 

COSθ=X coordinate/Hypotenuse

TANθ=Y coordinate/X coordinate 

NOW:::

#NOTE:: HERE HYPOTENUSE IS INDEPEDENT OF SIGN AS IT IS CONSIDERED AS LENGTH

(AND LENGTH IS ALWAYS CONSIDER AS POSITIVE)

QUADRANT DISTRIBUTION:

-------> In First Quadrant Y AND X Both Coordinate is positive hence SINθ is Positive 

(AS SINθ.COSECθ = Y coord./Hypotenuse = positive/Positive =Positive 

AS COSθ,SECθ= X coord./Hypotenuse = positive/Positive =Positive 

AS TANθ ,COTθ= Y coord./X coord. = positive/Positive =Positive )

------->In Second Quadrant Y Coordinate is positive and x is Negative

(AS SINθ.COSECθ = Y coord./Hypotenuse = positive/Positive =Positive)

-------->In Third Quadrant Y,X Coordinate is Negative.

(AS TANθ ,COTθ= Y coord./X coord. = positive/Positive =Positive )

---------->In Second Quadrant X Coordinate is positive and Y is Negative

(AS COSθ,SECθ= X coord./Hypotenuse = positive/Positive =Positive)

### REMEMBERING TRICK####

RESPECTIVE ELEMENT WRITTEN ARE POSITIVE IN THEIR QUADRANT AND REST REFEREED AS NEGATIVE ON THAT PARTICULAR QUADRANT

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HOPE YOU GUYS UNDERSTAND WELL

STAY TUNED STUDY WELL

HAPPY LEARNING