Where are the asymptotes of f(x) = tan(4x − π) from x = 0 to x = pi over 2 ?
1 answer:
The asymptotes are where the graph is undefined. Since: tan(x) =sin(x)/cos(x)
It is where cos(4x-π) = 0
cos(4x-π) = 0 when the inside is -π/2 , π/2 , 3π/2
4x - π = π/2
4x = π/2 + π
4x = 3π/2
x = 3π/8
4x - π = 3π/2
4x = 3π/2 + π
4x = 5π/2
x = 5π/8
This ones outside the interval (5π/8 > π/2) , try -π/2
4x - π = -π/2
4x = -π/2 + π
4x = π/2
x = π/8
Asymptotes are π/8 and 3π/8
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