Find X-Intercept of y=atan(b(x-c))+d in Radians

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In summary, the conversation discusses how to determine the exact x-intercept of a tan graph in radian form when the d value does not equal 0. It is mentioned that there is no formula for finding the x-intercept when given the equation in the form above, but the general method is to rearrange it into the form x=something and plug in the values for a, b, and c. It is also mentioned that there are no "neat" answers in terms of pi or other exact values, and that graphing and tracing the zeros may be necessary. Finally, there is a brief discussion about the equation and the use of +c instead of -c in the solution for x.
  • #1
yourmom98
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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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  • #2
same way you get the zeros for any function: let y=0.
 
  • #3
whoops i need to edit it i mean as an exact value in radian form like pi/2 for example
 
  • #4
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!
 
  • #5
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! :mad:




:tongue:
 
  • #6
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?
 
  • #7
You need to take the equation

[tex]\arctan (b (x - c)) + d = 0[/tex]

and solve it for [itex]x[/itex], that is, rearrange it into the form

[tex]x = something[/tex]

Then plug in whatever values you have for [itex]b[/itex], [itex]c[/itex], and [itex]d[/itex]. Where do you get stuck when you try to do this?
 
  • #8
jtbell said:
You need to take the equation

[tex]\arctan (b (x - c)) + d = 0[/tex]

and solve it for [itex]x[/itex], that is, rearrange it into the form

[tex]x = something[/tex]

Then plug in whatever values you have for [itex]b[/itex], [itex]c[/itex], and [itex]d[/itex]. 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.)
 
  • #9
some simple algebra says: [tex]x=\frac{\tan^{-1}(-\frac{d}{a})}{b}+c[/tex]
 
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  • #10
yourdadonapogostick said:
some simple algebra says: [tex]x=\frac{\tan^{-1}(-\frac{d}{a})}{b}-c[/tex]

"+c," right?
 
  • #11
Brad Barker said:
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". :blushing:
 
  • #12
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 :smile:
 
  • #13
Brad Barker said:
"+c," right?
yea, oops. maybe i should proofread before i submit
 

1. What is an x-intercept?

An x-intercept is a point on a graph where the line or curve crosses the x-axis. It is the value of x when y is equal to zero.

2. What does "atan" stand for in the equation?

"atan" is an abbreviation for the trigonometric function arctangent, also known as inverse tangent. It is used to find the angle whose tangent is a given number.

3. What do b, c, and d represent in the equation?

b, c, and d are constants that affect the shape and position of the graph. b represents the slope, c represents the horizontal shift, and d represents the vertical shift.

4. How do you find the x-intercept of a trigonometric function?

To find the x-intercept of a trigonometric function, set y equal to zero and solve for x using algebraic methods or a graphing calculator.

5. Why is the x-intercept important in this equation?

The x-intercept is important because it tells us the value of x when the function crosses the x-axis, which can provide important information about the behavior of the function. In this equation, the x-intercept is useful in determining the period and phase shift of the graph.

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