Solve cos2xsinx=1: Simplifying and Finding X

  • Thread starter Thread starter CutiePieYum
  • Start date Start date
Click For Summary

Homework Help Overview

The problem involves simplifying and solving the equation cos(2x)sin(x) = 1, which falls under trigonometric identities and equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the simplification of the equation and explore the implications of the maximum values of cos(2x) and sin(x). Some question the feasibility of achieving the conditions for the equation to hold true.

Discussion Status

The discussion is ongoing, with participants offering different perspectives on the problem. Some have suggested graphing the functions or reformulating the equation into a cubic form, while others express uncertainty and seek additional guidance.

Contextual Notes

Participants note the constraints of the maximum values of the trigonometric functions involved and the potential need for further clues or hints to progress in solving the equation.

CutiePieYum
Messages
3
Reaction score
0

Homework Statement


Simplify AND Solve for X
cos2xsinx=1


Homework Equations


The triples, doubles


The Attempt at a Solution


cos2xsinx=1
(cos^2x-sin^2x)(sinx)=1
(-1x)(sinx)=1
-sinx=1
sinx= -1
?


..

:-/

Help.. :)
 
Physics news on Phys.org


The maximum absolute value of cos(2x) and sin(x) is 1. So the only way you can solve that is if cos(2x)=1 AND sin(x)=1 or cos(2x)=(-1) AND sin(x)=(-1). Is either of those possible? If so which one?
 


I have no idea may i have another clue
 


anyone?
 


CutiePieYum said:
I have no idea may i have another clue

Graph cos(2x) and sin(x) on [0,2pi]. Or do this cos^2(x)-sin^2(x)=1-2*sin^2(x). So you have (1-2*sin^2(x))*sin(x)=1. If sin(x)=u then you have (1-2*u^2)*u=1. That's a cubic equation for u. Can you find the real root?
 
Last edited:

Similar threads

Trigonometric equation solving 2cos x=tan x
  • · Replies 6 ·
Replies
6
Views
3K
Transforming sinx to sinx + cosx
  • · Replies 6 ·
Replies
6
Views
2K
Trigonometric Equations Problems - Rather Confused
  • · Replies 1 ·
Replies
1
Views
2K
Finding the Solution to an Equation: R.S = 1/1+cosx
  • · Replies 8 ·
Replies
8
Views
2K
Why Does This Trigonometric Identity Seem Incorrect?
  • · Replies 11 ·
Replies
11
Views
2K
How Do You Simplify Trigonometric Expressions Using Basic Identities?
  • · Replies 5 ·
Replies
5
Views
2K
Generel Solution of sinx+cos^2 x= 1
  • · Replies 8 ·
Replies
8
Views
2K
Solving Quadratic Trig Equation
  • · Replies 6 ·
Replies
6
Views
2K
How Many Solutions Does the Trigonometric Equation Have in the Given Interval?
  • · Replies 5 ·
Replies
5
Views
2K
Trig ((tanx - sinx)/sin^3x) = (1/(cosx - cos^2x))
  • · Replies 4 ·
Replies
4
Views
7K