# Tan x-intercepts

yourmom98
the tan graph is in the form y=atan(b(x-c))+d how do you determine the "EXACT" x-intercept of this graph in radian form when the d value does not equal 0 and is there a formula for finding the x-intercept when given the equation in the form above using the values of a,b,c and d which control the vertical/horizontal stretch/shift

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same way you get the zeros for any function: let y=0.

yourmom98
whoops i need to edit it i mean as an exact value in radian form like pi/2 for example

yourmom98 said:
whoops i need to edit it i mean as an exact value in radian form like pi/2 for example

well, in general, your answer is just going to have to be left in terms of arctangents, multiplied by some factor and then added to by another factor.

neat answers like pi/2 only come up only in special situations, unfortunately!

yourmom98 said:
whoops i need to edit it i mean as an exact value in radian form like pi/2 for example

and my mom is NOT 98!

:tongue:

yourmom98
okay so there are not going to be neat answers so is my only way to get a estimated answer in radian to graph it using a calculator and then trace the zeros? or is there a way to determine it without graphing?

Mentor
You need to take the equation

$$\arctan (b (x - c)) + d = 0$$

and solve it for $x$, that is, rearrange it into the form

$$x = something$$

Then plug in whatever values you have for $b$, $c$, and $d$. Where do you get stuck when you try to do this?

jtbell said:
You need to take the equation

$$\arctan (b (x - c)) + d = 0$$

and solve it for $x$, that is, rearrange it into the form

$$x = something$$

Then plug in whatever values you have for $b$, $c$, and $d$. Where do you get stuck when you try to do this?

that wasn't his equation.

it was a*tan(b(x-c) + d.

"a" is a stretching/shrinking factor. (i guess it's that there are only two missing letters between atan and arctan and the fact that i mentioned arctan that led you to this.)

some simple algebra says: $$x=\frac{\tan^{-1}(-\frac{d}{a})}{b}+c$$

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some simple algebra says: $$x=\frac{\tan^{-1}(-\frac{d}{a})}{b}-c$$

"+c," right?

Mentor
that wasn't his equation.

it was a*tan(b(x-c) + d.

"a" is a stretching/shrinking factor. (i guess it's that there are only two missing letters between atan and arctan and the fact that i mentioned arctan that led you to this.)

Oops. I've done too much computer programming in languages that call the arctangent function "atan".

yourmom98
yea it +c not -c so this gets me the so therefore i can now just like add or substract another period to this answer to get another x-intercept rite?

thx everyone