# Trig limits question

## Homework Statement

evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3

## The Attempt at a Solution

the answer in the textbook is 8/27
i figured they got that by raising 2 to the 3rd and 3 to the 3rd
but i'm not entirely sure what happens to the sin's

id really appreciate a worked out answer (that doesn't use l'hopital's rule)

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LCKurtz
Homework Helper
Gold Member

## Homework Statement

evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3

## The Attempt at a Solution

the answer in the textbook is 8/27
i figured they got that by raising 2 to the 3rd and 3 to the 3rd
but i'm not entirely sure what happens to the sin's

id really appreciate a worked out answer (that doesn't use l'hopital's rule)
We don't do worked out answers. But here's a hint: Presumably you know something about the limit of sin(x)/x as x → 0. Make use of that by multiplying and dividing by certain powers of x.

We don't do worked out answers. But here's a hint: Presumably you know something about the limit of sin(x)/x as x → 0. Make use of that by multiplying and dividing by certain powers of x.
well
lim
x->0 sinx/x = 1
the problem is that i don't know how to apply it to this question

LCKurtz
Homework Helper
Gold Member
well
lim
x->0 sinx/x = 1
the problem is that i don't know how to apply it to this question
What would be the limit of $\frac {\sin(2x)}{2x}$ as x → 0?

What would be the limit of $\frac {\sin(2x)}{2x}$ as x → 0?
that limit would be 1 as well
but i'm still not sure how it'd help

LCKurtz