Where are the asymptotes of f(x) = tan(4x βˆ’ Ο€) from x = 0 to x = pi over 2 ?

Question
Answer:
[tex]tan(4x- \pi )= \frac{sin(4x- \pi )}{cos(4x- \pi )} [/tex]

The asymptotes are where the graph is undefined. Since: tan(x) =sin(x)/cos(x)
It is where cos(4x-Ο€) = 0

cos(4x-Ο€) = 0 when the inside is -Ο€/2 , Ο€/2 , 3Ο€/2

4x - Ο€ = Ο€/2
4x = Ο€/2 + Ο€
4x = 3Ο€/2
x = 3Ο€/8

4x - Ο€ = 3Ο€/2
4x = 3Ο€/2 + Ο€
4x = 5Ο€/2
x = 5Ο€/8
This ones outside the interval (5Ο€/8 > Ο€/2) , try -Ο€/2

4x - Ο€ = -Ο€/2
4x = -Ο€/2 + Ο€
4x = Ο€/2
x = Ο€/8

Asymptotes are Ο€/8 and 3Ο€/8




solved
general 11 months ago 6011