What is the period of y equals -5 tan x?
y = -5tan(x) can also be written y/(-5) = tan(x). In other
words, the -5 just changes the y values and the orientation of the
graph (it flips tan(x) over the y axis and stretches the graph up
and down).
So -5tan(x), like tan(x), has a period of pi. This is because
tan is the y value divided by the x value at any given point on the
unit circle. At 0 degrees, x is at one and y is at zero, so tan0o =
0. As we travel counterclockwise around the unit circle, tan is
next equal to zero when x is equal to zero. This occurs halfway
around the circle at 180o, or (in radians) pi.