How to find tan(-pi)?

tan (-pi)

1 Answer
May 18, 2018

#0#

Explanation:

Apply the definition:

#tan(x) = \frac{sin(x)}{cos(x)}#

So,

#tan(-pi) = \frac{sin(-pi)}{cos(-pi)}#

Actually, you may notice that #-pi# and #pi# identify the same angle, since you're making half of a turn, either clockwise or counterclockwise, but still ending at #(-1,0)#. So, we may simplify the expression into

#tan(-pi) = tan(pi) = \frac{sin(pi)}{cos(pi)}#

Now, #pi# is a known value for trigonometric function, and I've actually already wrote the answer: since the angle #pi# is associated to the point #(-1,0)#, and for every point #P=(x,y)# identified by the angle #alpha# on the unit circumference you have #(cos(alpha),sin(alpha))=(x,y)#, we have

#(cos(pi),sin(pi))=(-1,0)#

and thus

#tan(-pi) = tan(pi) = \frac{sin(pi)}{cos(pi)} = \frac{0}{-1}=0#