Combining Sine Functions: Simplifying with Trigonometry

In summary, the conversation is about trying to write the expression sin(2x) + sin(2[x + π/3]) as a single function. The person is unsure how to do this and is concerned about merging two sine-wave functions into one. The solution involves using a trigonometry formula and reviewing basic trigonometric identities. Wolfram Alpha can also be helpful in finding the required identity.
  • #1
Benhur
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Summary:
I have the expression sin(2x) + sin(2[x + π/3]) and I have to write this in terms of a single function (a single harmonic, rather saying). But I don't know how to do this, and... it seems a little bit weird for me, because I'm merging two sine-wave functions into one. Doesn't the sum of sines result in a more complex body than a simple sine alone?

The exercise that I'm trying to solve says that I must use a trigonometry formula to solve.
 
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  • #3
Thank you, DrClaude. Now I got it.
 
  • #4
Wolfram Alpha sometimes helpful to remind yourself about trig identities: sin(a)+sin(b). (you might have to 'wade' through a lot of extraneous information before you find the required identity)
 
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1. What is a combination of sine functions?

A combination of sine functions is a mathematical expression that involves adding, subtracting, multiplying, or dividing two or more sine functions. Sine functions are trigonometric functions that describe the relationship between the angles and sides of a right triangle.

2. How do you simplify a combination of sine functions?

To simplify a combination of sine functions, you can use trigonometric identities and properties, such as the sum and difference identities, double angle identities, and half angle identities. These identities allow you to rewrite the expression in a simpler form.

3. What is the period of a combination of sine functions?

The period of a combination of sine functions is the smallest interval over which the function repeats itself. For a combination of sine functions, the period is determined by the lowest common multiple of the periods of the individual sine functions involved in the combination.

4. How do you find the amplitude of a combination of sine functions?

The amplitude of a combination of sine functions is the maximum distance of the function from the x-axis. To find the amplitude, you can use the amplitude formula: A = (max - min)/2, where max and min are the maximum and minimum values of the function, respectively.

5. What is the importance of studying combinations of sine functions?

Studying combinations of sine functions is important in many fields, such as physics, engineering, and mathematics. These functions can be used to model and analyze various real-world phenomena, such as sound waves, electromagnetic waves, and oscillations. Understanding combinations of sine functions also helps in solving more complex mathematical problems and developing new mathematical concepts and theories.

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