What is tan(-9pi)?

1 Answer
Mar 25, 2017

tan(-9pi)=color(green)(0)

Explanation:

When evaluating angles (specified in radians) any angle theta is equivalent to theta+2kpi for kin ZZ since an angle of 2pi represents a complete circle.

So when evaluating tan(-9pi) we can equate
color(white)("XXX")-9pi = -7pi=-5pi=-3pi=-pi=pi

That is
color(white)("XXX")tan(-9pi)=tan(pi)

Using the unit circle and an angle in standard position,
the angle pi is a point on the negative X-axis at (x,y)=(-1,0)

rArr tan(-9pi) = y/x = 0/(-1) = 0