Applied arithmetic progression in trigonometry

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Mathalcoholic

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Oct 18, 2020
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Hello,
I've come across an exercise that has caught my attention, however I haven't been able to answer it correctly yet. I'm currently studying trigonometry function and this exercise has arithmetic progression included in it.

Here's the exercise translated in english:
"Consider a sequence of numbers
a_n=sin(nxpi)/4, n=1,2,3,..., Prove without using any technical aids that
a_1=a_9=a_17."

Here's also a photo of the exercise:

Screenshot_20201018_123500.jpg
 
Mathalcoholic said:
Hello,
I've come across an exercise that has caught my attention, however I haven't been able to answer it correctly yet. I'm currently studying trigonometry function and this exercise has arithmetic progression included in it.

Here's the exercise translated in english:
"Consider a sequence of numbers
a_n=sin(nxpi)/4, n=1,2,3,..., Prove without using any technical aids that
a_1=a_9=a_17."

Here's also a photo of the exercise:

View attachment 22404
Click to expand...
Can you evaluate:

an+8 from the given expression of an?​

By the way, the given "sequence" is NOT an "arithmetic progression". What is one of the defining properties of "arithmetic progression"?
 
In addition to what Subhotosh Khan has asked you can you please tell me if sin( 2pi + x) = sin(x)??
 
Subhotosh Khan said:
Can you evaluate:

an+8 from the given expression of an?​

By the way, the given "sequence" is NOT an "arithmetic progression". What is one of the defining properties of "arithmetic progression"?
Click to expand...
If a constant quantity is added to or subtracted from each term of an Arithmetic Progression then the resulting terms of the sequence are also in A. P. with same common difference.
 
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