Question

How do you graph y=1/4tan(5x) ?

Answer 1

Hint:\[\frac{1}{4\tan{5x}} = \frac{1}{4}\cot{5x}\]

Answer 2

I'm confused... I was absent the day my teacher taught this

Answer 3

do you know the graph of tan(x)?

Answer 4

no

Answer 5

well, then you should start there
do you know what a function transformation is?

Answer 6

yes, and I also know that for tan, the period is pi

Answer 7

\(\bf {\color{blue}{ \cfrac{1}{4}}}tan({\color{red}{ 5}}x)\\ \quad \\
transformation \implies {\color{blue}{ amplitude}}\quad \textit{new period}=\cfrac{\textit{original period}}{{\color{red}{ 5}}}=\cfrac{\pi}{{\color{red}{ 5}}}\)

Answer 8

so you grab tan(x) and change its amplitude to that and change its period accordingly :)

Answer 9

notice, you have no shifts, so, the graph will remain in place, it'll just become thinner

Answer 10

I think I understand, but I'm a bit confused. For other trig functions such as sin, we use a t chart. for the x values, it would start 0, pi/2, pi, 3pi/2, and 2pi. for the y values, it would be 0, 1,0,-1, and 0. So for tan(x) what would the values be?

Answer 11

well, tangent is a function based on sine and cosine
the cosine is the denominator
whenever the denominator turns to 0, the fractions becomes undefined
so wherever cosine is 0, tangent is undefined, or that is it has an asymptote

so you can just fine the values where cosine is defined, and use that as the plot points

say....whenever cosine is say 1 or -1, that is at \(\bf 0, \pi, 2\pi\) and so on

Answer 12

oh, so the y values would be the same as the y values of cosine? 1, 0, -1, 0, and 1 ?
okay, that makes so much more sense! thank you! But how do you find the vertical asymptotes of this graph?

Answer 13

Also, since cotangent is the opposite of tangent, would the y values be the same?

Answer 14

whenever cosine is 0, the denominator will be 0 for the tangent function, the function will be undefined, thus an asymptote

Answer 15

their range is pretty much the same, yes -> http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ0YW4oeCkiLCJjb2xvciI6IiNEMTE5MTkifSx7InR5cGUiOjAsImVxIjoiY290KHgpIiwiY29sb3IiOiIjMUUxOEQ5In0seyJ0eXBlIjoxMDAwfV0-

Answer 16

so, for this graph, the x values would be 0, pi/2, pi, 3pi/2, and 2pi while the denominator or the y values would be 0, pi/2+ pi/5, pi + pi/5, 3pi/2 + pi/5, and 2 pi + pi/5 ?

Answer 17

well... for this graph... this graph shows no shifts... so the "x" values will be the same as for the parent tan(x) fucntion

the most noticeable change will be the period change, to 1/5 of the original
the amplitude is 1/4 of the original, so it'll "expand" the graph a bit

Answer 18

okay, i think my main question that troubles me is, what are the x and y values of the parent tan(x) function