Graph y = -tan(π/2). What are its vertical asymptotes?
How would I graph the function?
Thanks!
$\displaystyle y=-\tan\left(\frac{n}{2}\right)=\ -\frac{\sin\left(\frac{n}{2}\right)}{\cos\left(\fra c{n}{2}\right)}$ and if you know the half angle formulas, which state
$\displaystyle \sin\left(\frac{n}{2}\right)=\pm\sqrt{\frac{1-\cos(n)}{2}}$
$\displaystyle \cos\left(\frac{n}{2}\right)=\pm\sqrt{\frac{1+\cos (n)}{2}}$
Then $\displaystyle -\frac{\sin\left(\frac{n}{2}\right)}{\cos\left(\fra c{n}{2}\right)}=\pm\sqrt{\frac{1-cos(n)}{1+cos(n)}}=\pm\sqrt{\frac{1-cos(n)}{1+cos(n)}*\frac{1-cos(n)}{1-cos(n)}}=\pm\sqrt{\frac{(1-cos(n))^2}{1-cos^2(n)}}$
$\displaystyle =\pm\sqrt{\frac{(1-cos(n))^2}{sin^2(n)}}=\frac{1-cos(n)}{sin(n)}$
Now finding your asymptotes should be easy (sin(n)=0) and graphing this by hand, well I would graph the numerator and then the denominator, and then divide the corresponding y values point by point for an accurate sketch
as theemptyset has just pointed out, seems as though i may have misinterpretted that pi for an n, making this wrong and yeah... sorry for that