Solve Max of sin(x) + sin(2x): Get Answer Now!

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In summary, the conversation discusses finding the maximum of a function without a computing device, specifically Y = sin(x) + sin(2x). Various methods are attempted, including using Euler's formula and drawing a graph, but none are successful. Mathematica provides a solution using the FindMaximum function. Another person suggests solving for dy/dx = 0 and substituting cos(2x) as 2cos^2(x) - 1, resulting in a quadratic to solve. The conversation ends with the realization that this method was overlooked initially.
  • #1
Constantinos
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This is not homework question, just curious about it though. This problem is supposed to be done without a computing device and was in an exam at a university course. I don't think it can be done.

Homework Statement


I want to find the maximum of this function:

Y = sin(x) + sin(2x)

Homework Equations


The Attempt at a Solution



Attempted sin(2x) = 2sinx*cosx, tried to draw it, tried to go euler's formula, no luck whatsoever (of course I take the derivative!)

Mathematica gives me this:

FindMaximum[Sin[x] + Sin[2*x], {x, 0}]

Out[1]= {1.76017, {x -> 0.935929}}

Any ideas? It really seems simple, but I just can't figure it out...

Thanks!
 
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  • #2
Why don't you just solve dy/dx = 0 and then sub cos(2x) as 2cos2-1 ?

You should get a quadratic in cosx to solve.
 
  • #3
rock.freak667 said:
Why don't you just solve dy/dx = 0 and then sub cos(2x) as 2cos2-1 ?

You should get a quadratic in cosx to solve.

Lol where is my mind! Thanks :P
 

FAQ: Solve Max of sin(x) + sin(2x): Get Answer Now!

What does "solve max of sin(x) + sin(2x)" mean?

The phrase "solve max" means to find the maximum value of a function. In this case, we are looking for the maximum value of the function sin(x) + sin(2x).

How do I solve for the maximum value of this function?

To solve for the maximum value, we need to take the derivative of the function and set it equal to 0. Then, we can solve for x and plug it back into the original function to find the maximum value. In this case, the maximum value occurs when x = π/6 or x = 5π/6.

Can you provide the steps to solve this problem?

Sure! First, we take the derivative of the function sin(x) + sin(2x) which is cos(x) + 2cos(2x). Then, we set this equal to 0 and solve for x to get x = π/6 or x = 5π/6. Finally, we plug these values back into the original function to find the maximum value of √3 + 1.

Is there a graphical way to solve this problem?

Yes, we can also use a graphing calculator or software to graph the function and visually determine the maximum value. From the graph, we can see that the maximum value occurs when x = π/6 or x = 5π/6, and the maximum value is √3 + 1.

Can this problem be solved using any other methods?

Yes, there are multiple methods for solving this problem such as using trigonometric identities or using the first derivative test. However, taking the derivative and setting it equal to 0 is the most straightforward method.

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