Solving for x: Find the Solution to 2sinx-sin2x=4/∏

  • Thread starter maff is tuff
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In summary, to solve the equation 2sinx-sin2x=4/∏, you can use the identity sin2x=2sinxcosx to transform the equation into sinx(1-cosx)=2/∏. Simplify this equation to get sin²x(1-cosx)²=4/∏² and then expand to get a quartic equation in terms of cosines. From there, you can use algebraic techniques to solve for the values of x that satisfy the equation.
  • #1
maff is tuff
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1

Homework Statement



Solve for x: 2sinx-sin2x=4/∏

Homework Equations



sin2x=2sinxcosx

The Attempt at a Solution



2sinx-sin2x=4/∏

2sinx-2sinxcosx=4/∏

2sinx(1-cosx)=4/∏

sinx(1-cosx)=2/∏

And I get stuck here. Any suggestions or mistakes that I made? Thanks in advance.
 
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  • #2
Square [sinx(1-cosx)=2/∏], and modify the expression from sines to coses.
You'll end up having a quartic equation with two real solutions.
 
  • #3
Atran said:
Square [sinx(1-cosx)=2/∏], and modify the expression from sines to coses.
You'll end up having a quartic equation with two real solutions.
So:

sinx(1-cosx)=2/∏

sin²x(1-cosx)²=4/∏ ²

sin² x(1-2cosx+cos² x)=4/∏ ²

(1-cos² x)(1-2cosx+cos² x)=4/∏ ²

1-2cosx+cos² x-cos² x+2cos³ x-cos^4x=4/∏ ²

1-2cosx+2cos^3x-cos^4x=4/∏ ²

Sorry but now I'm stuck here. Thanks for you help so far but can you give me another hint how to get past this part? Thanks.
 

1. What is the equation 2sinx-sin2x=4/∏?

The equation 2sinx-sin2x=4/∏ is a trigonometric equation that involves the sine function and the value of pi (π). It is typically used to solve for the variable x.

2. How do you solve for x in this equation?

To solve for x in this equation, you can use various algebraic and trigonometric techniques such as factoring, substitution, and the double-angle formula. It is important to remember to isolate the variable on one side of the equation and simplify the other side to find the solution.

3. Can this equation have multiple solutions?

Yes, this equation can have multiple solutions. Since the sine function is a periodic function, it repeats itself every 360 degrees (or 2π radians). Therefore, there may be multiple values of x that satisfy the equation.

4. What are the possible values of x that can satisfy this equation?

The possible values of x that can satisfy this equation depend on the given range or interval. For example, if the range is from 0 to 360 degrees, the possible values of x can be any angle within that range that satisfies the equation. However, if no range is specified, the possible values of x can be any real number.

5. Can this equation be solved graphically?

Yes, this equation can be solved graphically by plotting the given equation and finding the points of intersection between the graph and the x-axis. However, this method may not always be accurate and should be used in combination with other algebraic or trigonometric methods.

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