Question

if given sin(x)=3/4 and we wanna find cos(x) which is located in quadrant 4... i can use sin(x)^2 + cos(x)^2 = 1 and get something like -sqrt(7)/4
but if i wanted to do this the way of sin(x) = opp/hyp and cos(x) = adj/hyp how come the answer wont be the same? is this cause the 2nd way only applys to right triangles? and the 1st applys to any situation?

Answer 1

using formula u get 2 values
-sqrt(7)/4 and sqrt(7)/4
u choose 1 based on quadrant,so here sqrt(7)/4

Answer 2

No you could do that way also but if you are given that x is in 4th quadrant
then sin x should be negative
just find cos x using positive sin x using a right triangle
cos x is positive in 4th quadrant, so we don't need to change sign

Answer 3

hmm it seems both ways do work.. but i remember a while back there was a example that didtn work for both for some random reason