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Locating a Point in Cartesian Plane

If theta =-3 ...

Question

If cot theta = - 3/4 and theta is not in the 2nd quadrant then 5 sin theta + 10 cos theta + 9 sec theta + 16cosec theta - 4 cot theta =

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Solution

First of all in these type of question you need to understand that sign comes from the quadrant here as given cot@= -3/4 and @ is not in the 2nd quadrant then it can only be in the 4th quadrant,now in 4th quadrant cos and sec are positive and others will be negative (you must know ASTC rule ) we know cot@=base/perpendicualr so here base =3 and perpindcular is 4 (can't take negative as they are lengths but ultimately while writing them we will use quadrants concept) so hypotenuse =5
from here
sin@=-4/5 cos@=3/5 sec@=5/3 cosec@= -5/4 put these values
5(-4/5)+10(3/5)+9(5/3)+16(-5/4)-4(-3/4)
=0

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