Thread: trig four quadrants

Hello everyone!

I've found the answer to this just need to know if its in the right term

Given that cosec θ = −2, tan θ = 1/3√3

and −π < θ < π, find the exact
value of the angle θ in radians. Justify your answer.

answers are

cosec = 1/sin = -1/2 (which means its in the 3rd or 4th quadrant)
tan = 1/3√3 (which means its in the 1st or 3rd quadrant)

this means that theta is in the 3rd quadrant

but is it -1/6pi or -5/6pi? because each of their values is either +/- 1/6pi but surely that cant be right because -1/6pi is -30 which is not in the 3rd quadrant, could someone just classify this for me! cheers

hi emakarov, sorry i don't think i explained very well,

first off i meant (1/3) * √3 which i think is the same as what you wrote 1 / √3

secondly i what i was trying to say was that both these values

sinθ = -1/2 = -1/6pi and

tanθ = 1/√3 = 1/6pi

but this is where i get stuck, because i have two values which are either positive or negative of 1/6 pi and which are neither in the third quadrant so i thought it must be -5/6pi (-150 degrees)

but this is where i need help

hi skeeter, please explain further. many thanks

Thanks for your help emakarov,

That has cleared a lot of things up, looks like I'm going to have to study harder!!