Question

For what value(s) of x does y = 0 for the function tan(x)?

Answer 1

So We Know That tan(x) Equals

$\tan(x) = \frac{ \sin(x) }{ \cos(x) }$
We Can Use Logic, We Know That Anything That Makes The Denominator 0, Will Not Work, So We Need To Know What Makes Sin(x) equal to 0 and Cos(x) equal to 1 or -1 BUT NOT 0

$\sin(0) = 0 \: \cos(0) = 1 \\ \sin(180) = 0 \: \cos(180) = - 1 \\ \sin(360) = 0 \: \cos(360) = 1 \\ \sin( - 180) = 0 \: \cos( - 180) = - 1 \\ \sin( - 360) = 0 \: \cos( - 360) = 1$
$\cos(90) = 0 \\ \cos( - 90) = 0 \\ \cos(270) = 0 \\ \cos( - 270) = 0$
We Didn't Want Cosine To equal Zero Because Then We Get

$\tan(x) = \frac{ \sin(x) }{ \cos(x) } \\ \tan(x) = \frac{ \sin(90) }{ \cos(90) } \\ \tan(x) = \frac{1}{0} \\ \tan(x) = indeterminate$

THE ANSWER IS C : -360°,-180°,0°,180°,360°