Here, -240^circ=(-180^circ)+(-60^circ)=>II^(nd)Quadrant
But , +240^circ=180^circ+60^circ=>III^(rd)Quadrant
So ,
color(red)(sinx,cosx ,secx,cscx ,are-ve )andcolor(blue)( tanx,cotx,are +ve
(1)sin(-240^circ)=-sin240^circto[becausesin(-theta)=-sintheta]
color(white)(=>sin(-240^circ))=-sin(180^circ+60^circ)toIII^(rd)Quadrant
color(white)(=>sin(-240^circ))=-(-sin60^circ)
=>sin(-240^circ)=sin60^circ=sqrt3/2
(2)cos(-240^circ)=cos240^circto[becausecos(-theta)=costheta]
color(white)(=>sin(-240^circ))=cos(180^circ+60^circ)toIII^(rd)Quadrant
=>cos(-240^circ)=-cos60^circ=-1/2
(3)csc(-240^circ)=-csc240^circto[becausecsc(-theta)=-csctheta]
color(white)(=>sin(-240^circ))=-csc(180^circ+60^circ)toIII^(rd)Quadrant
color(white)(=>sin(-240^circ))=-(-csc60^circ)
=>csc(-240^circ)=csc60^circ=2/sqrt3
(4)sec(-240^circ)=sec240^circto[becausesec(-theta)=sectheta]
color(white)(=>sin(-240^circ))=sec(180^circ+60^circ)toIII^(rd)Quadrant
=>sec(-240^circ)=-sec60^circ=-2
(5)tan(-240^circ)=-tan240^circto[becausetan(-theta)=-tantheta]
color(white)(=>sin(-240^circ))=-tan(180^circ+60^circ)toIII^(rd)Quadrant
color(white)(=>sin(-240^circ))=-tan60^circ
=>tan(-240^circ)=-tan60^circ=-sqrt3
(6)cot(-240^circ)=-cot240^circto[becausecot(-theta)=-cottheta]
color(white)(=>sin(-240^circ))=-cot(180^circ+60^circ)toIII^(rd)Quadrant
color(white)(=>sin(-240^circ))=-cot60^circ
=>cot(-240^circ)=-cot60^circ=-1/sqrt3
