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

[Septimra]

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.

 

[Simon Bridge]

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?

 

[Septimra]

Haha whilst formulating my response... I saw the light! Thank you so much!

Great way to start the day, and good one to ya!

 

[Simon Bridge]

Often the way - well done.