Friday, 9 November 2012

Trigonometrical ratios for related angles


Trigonometrical ratios for related angles

360o Corresponds to one full revolution.sine of angles of  360o+45o;720o+45o;1080o+45o are equal to sine of 45o.This is so far the other trigonometrical ratios.That is,When an angle exceeds 360o,it can be reduced to an angle between 0o and 360o by wiping out integral multiples of 360o

sin(- θ) = -sinθ

sin(90- θ)=cos θ

sin(90+ θ)=cos θ

sin(180- θ)=sin θ

sin(180+ θ)= -sin θ

sin(270- θ)= -cos θ

sin(270+ θ)=-cos θ

sin(360- θ)= -sin θ

cos(- θ) = cos θ

cos(90- θ)=sinθ

cos(90+ θ)= -sinθ

cos(180- θ)= -cos θ

cos(180+ θ)= -cos θ

cos(270- θ)= -sinθ

cos(270+ θ)=sinθ

cos(360- θ)= cos θ

tan(- θ) = -tan θ

tan(90- θ)=cotθ

tan(90+ θ)= -cotθ

tan(180- θ)= -tan θ

tan(180+ θ)= tan θ

tan(270- θ)= cotθ

tan(270+ θ)= -cotθ

tan(360- θ)= -tan θ

cosec(90+ θ)=sec θ

cosec(180- θ)=cosec θ

cosec(180+ θ)= -cosec θ

cosec(270- θ)= -sec θ

cosec(270+ θ)=-sec θ

cosec(360- θ)= -cosec θ

sec(- θ) = sec θ

sec(90- θ)=cosecθ

sec(90+ θ)= -cosecθ

sec(180- θ)= -sec θ

sec(180+ θ)= -sec θ

sec(270- θ)= -cosecθ

sec(270+ θ)=cosecθ

sec(360- θ)= sec θ

cot(- θ) = -cotθ

cot(90- θ)=tanθ

cot(90+ θ)= -tanθ

cot(180- θ)= -cot θ

cot(180+ θ)= cot θ

cot(270- θ)= tanθ

cot(270+ θ)= -tanθ

cot(360- θ)= -cot θ


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