How to know the quadrant $\sec(-\pi/4)$ lies in?
By John Parsons •
It is in quadrant four and since the angle is negative it moves clockwise but how do you know it is in quadrant four? For instance, I know $11\pi/6$ is in quadrant four because I divide $11$ by $6$ and get $1.833333$ which is greater than $3\pi/2$, but when I take $1$ divided by $4$ or $pi$ divided by $4$, I thought that would mean it is in the first quadrant.
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$\begingroup$It is the angle $-\pi/4$ that belongs in the fourth quadrant, not its secant.
If you have a negative angle, just add $2\pi$ until you get a positive number (or $0$). In this case $$ -\frac{\pi}{4}+2\pi=\frac{7\pi}{4} $$ and $$ \frac{3\pi}{2}<\frac{7\pi}{4}<2\pi $$
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