Where are the asymptotes of f(x) = tan(4x β 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
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11 months ago
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