SOLUTION: How to define a numerical point E(t) in the numerical circle if ctgt = 1, cost < 0?

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Question 939875: How to define a numerical point E(t) in the numerical circle if ctgt = 1, cost < 0?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
cot%28t%29=1
since
cot%28t%29=1%2Ftan%28t%29, we have
1%2Ftan%28t%29=1
tan%28t%29=1 => t=45°

for the point E%28t%29 in the numerical circle the x is cos%28t%29+ and y-coordinate is sin%28t%29:

so, the point E%28t%29 in the numerical circle if t=45° is:
(sqrt%282%29%2F2,sqrt%282%29%2F2)


given:
cos%28t%29%3C0
cos is negative for 90+%3Ct%3C270°

the point E%28t%29 has cos%28t%29%3C0 will be between points (0,1) and (0,-1)
it will be negative if 2pi%2F3%3C=t%3C=4pi%2F3 or 120+%3C=t%3C=240°

the point E%28t%29 is at any point starting with (-1%2F2,sqrt%283%29%2F2) and going to the point (-1%2F2,-sqrt%283%29%2F2)