Explanation:
a) Tangent equals sine divided by cosine. Therefore:
tan(-t) = sin(-t) / cos(-t)
b) Using the fact that sin(-t) = -sin(t) and cos(-t) = cos(t):
tan(-t) = -sin(t) / cos(t)
tan(-t) = -tan(t)
c) A function is symmetric about the origin if f(-x) = -f(x) (in other words, if it's an odd function). Therefore, y = tan(t) is symmetric about the origin.