How do I work out 3ii

[ivory merlin]

Struggling with Proof of sequences

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[tall barn]

So basically you know that sin is periodic every 2 pi

so it has same value for n = 0 and n = 12

[ivory merlin]

So essentially your saying it repeats itself every 360 degrees

sorry I think the radians part gets me a little confused

[tall barn]

yeah just by the property of sin

yeah no it’s ok

[ivory merlin]

Ok I get that

[tall barn]

You’ll get used to it in time

so effectively all you need to do is sub into a value of n something that will make the value of sin (2pi)

and your first n = 0 for simplicity

[ivory merlin]

Yeah

[tall barn]

so what’s ur value of n

[ivory merlin]

I’m not sure. What am I subbing in n=0 into

[tall barn]

well no ok so basically if you imagine the graph of sine

It starts a new cycle at 0, 2pi (360), 4pi (720) …

so this sequence is the same

It will start a new cycle at the same points

[ivory merlin]

yes

[tall barn]

So it’s asking for the number of terms the sequence repeats after

Just picking an easy value of n = 0 is when the cycle starts again

Now

When does the cycle repeat again?

[ivory merlin]

At 2pi

[tall barn]

exactly

[ivory merlin]

So how do I work out the value is the only part I’m confused about

[tall barn]

And you know that in the sequence the thing inside the sin is n pi /6

And that has to be equal to 2 pi

[ivory merlin]

Ohhhh ok

[tall barn]

So n = 12

So if you think

The n = 0 term is the same as n = 12

N = 1 same as n = 13

Etc ..

Due to the periodicity of sine

[ivory merlin]

Yes I understand

Thanks alot

[tall barn]

No problem