Pre calc

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How many times does the red graphs period repeat

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@gilded breach

[pearl dagger]

4.5 times

well

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Ok so how would I calculate the length of one period

Since my teacher said it repeats 3 times but I dont see it

[pearl dagger]

what’s the context of this problem

[fast tinsel]

Well it asking for the similarity between both graphs

And finding the period is the only way to find the horizontal stretch

[pearl dagger]

the period is when the graph goes back to the point it started

[fast tinsel]

Since Period = 2pi/ absolute value of B

[pearl dagger]

it’s like one complete cycle and it’s back at the value it started at

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Yeah

But how do I know where it starts and where it ends

[pearl dagger]

starting from the y axis, u see its at 12

so it’s (0,12)

now, what is the next point that y will be 12

that’s the period

[fast tinsel]

So 4 periods?

Or 4 repetitions

My stuff is in french but this is the work done for the question

And this is where my teacher said that it was 3 repetitions

[pearl dagger]

what’s m supposed to be

[fast tinsel]

Thats a pi symbol 🥲

lol

She was talking very quickly

[pearl dagger]

ok i see why

the distance the red graph travelled in 3 periods was 2 pi

so she divided it by 3 to get the period for just 1

[fast tinsel]

Isnt that still 4 bumps

[pearl dagger]

think of it as a wave

this is very similar to a physics concept on waves

it’s like going up and down

the graph starts up high, goes down, then goes back up where it started, marking 1 period (u can also call it like a oscillation)

[fast tinsel]

so the end of one of the waves is the beginning of the other one

[pearl dagger]

yass

u can also think of urself just jumping in the air

u start on the ground, go up in the air, then end back on the ground - marking 1 complete period

if u keep jumping and it’s kinda like a function

do u understand my goofy examples

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But doesent the 2pi point clip through half of the wave

Kinda yeah

[pearl dagger]

i see why u could question that

looking at the graph at 0, it starts at 12. so the end of a period is also gonna be at 12

[fast tinsel]

Ohh yeah I see it

So the stuff before X is 0 is just leftovers of another period?

[pearl dagger]

yeah lol u can say that

if u wanted to, u could look at the period from another point but it’s best starting from x=0

[fast tinsel]

I mean how I say it before it that the period before 0 is about half a period and the period after 2pi is another half so combined its one period