Standard answer for integral of cos(2deta)cos(ndeta)

In summary, the integral of cos(2deta)cos(ndeta) can be solved using the trigonometric identity cos(a)cos(b) = (1/2)(cos(a-b) + cos(a+b)). It can also be solved by substitution, where u = 2deta and du = 2deta. There is no specific range of values for deta and n for the integral to be solvable, but the resulting solution may involve difficult trigonometric functions. Integration by parts can also be used, but other methods may be more efficient. Real-world applications for this integral can be found in fields such as physics, engineering, and mathematics to model and solve problems involving periodic functions and in signal processing to
  • #1
stan
18
0
Hi

does anyone knows the standard answer for

integral of cos(2deta)cos(ndeta) from 0 to 180 degress?

for instance for integral of sin(ndeta)sin(deta) 0 to 180 degress, when n=1, it is 90 degress and when n not equals 1, it is 0...

thanks
 
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  • #2
Have you tried using integration by parts?
 
  • #3
What's a "deta" or an "ndeta"? What's your variable of integration?

You might want to review your trig identities... there's one that makes this kind of integral really easy.
 

1. How do you solve the integral of cos(2deta)cos(ndeta)?

The solution to this integral involves using the trigonometric identity cos(a)cos(b) = (1/2)(cos(a-b) + cos(a+b)). In this case, a = 2deta and b = ndeta.

2. Can the integral of cos(2deta)cos(ndeta) be solved by substitution?

Yes, the integral can be solved by using the substitution u = 2deta and du = 2deta. This will lead to the integral becoming (1/2)∫cos(u)cos(nu)du, which can then be solved using the trigonometric identity mentioned in the previous answer.

3. Is there a specific range of values for deta and n in order for the integral to be solvable?

No, the integral can be solved for any values of deta and n. However, the resulting solution may involve trigonometric functions that are difficult to integrate further.

4. Can the integral of cos(2deta)cos(ndeta) be solved using integration by parts?

Yes, the integral can be solved using integration by parts, but it may not be the most efficient method. Other methods, such as using trigonometric identities or substitution, may be easier to use.

5. Are there any real-world applications for the integral of cos(2deta)cos(ndeta)?

Yes, this integral can be used in various fields such as physics, engineering, and mathematics to model and solve problems involving periodic functions. It can also be used in signal processing to analyze signals with multiple frequencies.

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