Express sin4x in terms of sinx?

  • Context: Undergrad 
  • Thread starter Thread starter kgh0st
  • Start date Start date
  • Tags Tags
    Terms
Click For Summary

Discussion Overview

The discussion revolves around the problem of expressing sin(4x) in terms of sin(x). Participants explore different approaches and considerations related to this trigonometric expression, with a focus on homework-related challenges in trigonometry and calculus.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant requests assistance in expressing sin(4x) in terms of sin(x), indicating difficulty with the problem.
  • Another participant provides a hint that sin(4x) can be expressed as 2 sin(2x) cos(2x).
  • A different participant argues that sin(4x) cannot be expressed solely in terms of sin(x), but can be expressed in terms of both sin(x) and cos(x), noting that sin(2nx) generally requires both functions for n ≥ 1.
  • In contrast, a later reply suggests that it is possible to express sin(4x) in terms of sin(x) alone by using the identity cos(x) = +sqrt(1-sin^2(x)).

Areas of Agreement / Disagreement

Participants express differing views on whether sin(4x) can be expressed solely in terms of sin(x). There is no consensus on this issue, as some argue it is possible while others maintain it is not.

Contextual Notes

Participants reference identities and relationships between sine and cosine functions, but the discussion does not resolve the mathematical steps or assumptions involved in these expressions.

kgh0st
Messages
1
Reaction score
0
express sin4x in terms of sinx?

Alright so I am working on my homework tonight (i'm in trig/calc), and I get everything done but the last problem. Anyways, I've been working on this for a while now and I can't even get an idea of where to start. Anyways, he says we need to express sin4x in terms of sinx. Can anyone help me out as to how to do this?

Thanks in advance.
 
Physics news on Phys.org
HINT:

\sin 4x = 2 \sin 2x \cos 2x
 
kgh0st said:
Alright so I am working on my homework tonight (i'm in trig/calc), and I get everything done but the last problem. Anyways, I've been working on this for a while now and I can't even get an idea of where to start. Anyways, he says we need to express sin4x in terms of sinx. Can anyone help me out as to how to do this?

Thanks in advance.
I don't think sin(4x) can be expressed in terms of only sin(x). It can, however be expressed in terms of sin(x), and cos(x).
In general, sin(2nx), where n is a natural number that's greater than or equal to 1, can be expressed in terms of sin(x), and cos(x), but not sin(x) alone.
sin((2n + 1)x), n >= 0, however can be expressed in terms of only sin(x).
 
Well, actually, it can, since cos(x) = +sqrt(1-sin^2(x))
 

Similar threads

MHB Express in terms of sine function of f(x)=sinx+cosx
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How was this expression differentiated?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Linear approximation higher order terms
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What would a calculus author have to say on ##\int r^2dm##?
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Expressing an integral in terms of gamma functions
  • · Replies 1 ·
Replies
1
Views
3K
Phase space of a harmonic oscillator and a pendulum
  • · Replies 5 ·
Replies
5
Views
2K
Mathematica How to neglect specific terms in an expression?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Differentials of order 2 or bigger that are equal to 0
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Advice toward Mastering Challenging Vector Calc Problems
  • · Replies 4 ·
Replies
4
Views
2K
Help With Negative Phases in a Numerical Term
  • · Replies 1 ·
Replies
1
Views
2K