Solve for x between 0 , and 2pi the next equation?

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

Homework Help Overview

The discussion revolves around solving the equation cos x + √3 sin x = √2 for x in the interval [0, 2π]. Participants explore the transformation of the equation into a sine function format and express uncertainty about the steps involved in solving for x.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conversion of the original equation into the form sin(x + π/6) = √2/2 and question the validity of this transformation. There are attempts to clarify the steps taken to reach this form and the relevance of trigonometric identities.

Discussion Status

The discussion is ongoing, with participants providing guidance on the use of the homework template and the importance of showing work. There is a mix of confusion and attempts to clarify the process, with no clear consensus on the next steps or the correctness of the transformations made.

Contextual Notes

Some participants express confusion about relevant formulas and the steps taken to manipulate the original equation. There is mention of a need to adhere to homework presentation guidelines, indicating that the original poster may not have provided sufficient detail in their initial post.

luigihs
Messages
86
Reaction score
0
Solve for x between 0 , and 2pi the next equation?

cos x + square root(3) sinx = square root(2)

sin(x+ (pi/6)) = 1/sqrt2 <-- but then I don't know what to do this what I think should do, but I am not sure how to solve x help me thanks!
 
Physics news on Phys.org


You need to present your homework using the homework template where you state the problem, show some relevant formula that you might use to solve it and show an attempt.

I don't see how you got the sin(x+pi/6)=1/sqr(2) result from your original equation.
 


luigihs said:
Solve for x between 0 , and 2pi the next equation?

cos x + square root(3) sinx = square root(2)

sin(x+ (pi/6)) = 1/sqrt2 <-- but then I don't know what to do this what I think should do, but I am not sure how to solve x help me thanks!
So sin(x + π/6) = √2/2

Can you solve sin(u) = √2/2?

You've done all the hard work. The rest is easy.
 


jedishrfu said:
You need to present your homework using the homework template where you state the problem, show some relevant formula that you might use to solve it and show an attempt.

I don't see how you got the sin(x+pi/6)=1/sqr(2) result from your original equation.

Im really confused I don't even know any relevant formula I just tried to move the x
 


Mark44 said:
So sin(x + π/6) = √2/2

Can you solve sin(u) = √2/2?

You've done all the hard work. The rest is easy.

is this right? because somebody said early before that I was wrong... sin (u) = 0.707 ?
 


jedishrfu said:
You need to present your homework using the homework template where you state the problem, show some relevant formula that you might use to solve it and show an attempt.
Good advice. luigihs, the template is there for a reason - don't just blow it away...
jedishrfu said:
I don't see how you got the sin(x+pi/6)=1/sqr(2) result from your original equation.
He divided both sides of the equation by 2 to get (1/2)sin(x) + (√3/2)cos(x) = √2/2, and then replaced 1/2 by cos(π/6) and √3/2 by sin(π/6). It would have been helpful if he had shown his steps.
 


Sorry for what is the answer 0.707 ? I don't know how to do the operation
 


Mark44 said:
Good advice. luigihs, the template is there for a reason - don't just blow it away...

He divided both sides of the equation by 2 to get (1/2)sin(x) + (√3/2)cos(x) = √2/2, and then replaced 1/2 by cos(π/6) and √3/2 by sin(π/6). It would have been helpful if he had shown his steps.

Thanks I didn't see that. I kept thinking to square both sides but then I was still left with a puzzle. Its been a long time since I played with trig problems.
 


@ luigihs,

If \displaystyle \ \sin(\theta)=\frac{\sqrt{2}}{2}\,,\ then what is θ ?
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
1K
Replies
4
Views
2K
Replies
3
Views
2K
  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 40 ·
2
Replies
40
Views
5K
Replies
7
Views
2K
Replies
4
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K