Solve Trig Asymptotes: Find Equation on -pi < x < pi

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Homework Help Overview

The problem involves finding the equations of the asymptotes for the function tan(2 sin x) within the interval -pi < x < pi.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set cos(2 sin x) = 0 to find asymptotes but notes a discrepancy between their calculations and the number of asymptotes observed in the graph. Some participants suggest considering the properties of the tangent function and how often 2 sin x reaches specific values that create asymptotes.

Discussion Status

Participants are engaging in a productive exploration of the problem, with some guidance offered regarding the behavior of the tangent function and its asymptotes. The discussion reflects a mix of attempts and insights without reaching a definitive conclusion.

Contextual Notes

The original poster's calculations suggest a limited number of asymptotes, while the graph indicates more, prompting questions about the periodic nature of the sine function and its implications for the tangent function.

Septimra
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Homework Statement



Find the equation of the asymptotes.
On the interval -pi < x < pi

Homework Equations



tan(2 sin x)

The Attempt at a Solution



sin(2 sin x)/cos( 2 sin x)

Set cos( 2 sin x) = 0

2 sin x = arccos(0) = pi/2
2 sin x = arccos(0) = -pi/2

x = +-(arcsin pi/4)

But these are only but two asymptotes on the interval -pi < x < pi of tan( 2 sin x)-- yet when graphed; there are 4 observed.
 
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Use what you know of the tangent function directly.
tan has assymtotes when it's argument is a particular series of numbers - what are they?
2sin(x) can only evaluate to two of those numbers - what are they?
How many times does 2sin(x) visit each of those numbers in the interval?
 
Haha whilst formulating my response... I saw the light! Thank you so much!

Great way to start the day, and good one to ya!
 
Often the way - well done.
 

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