10th grade sinus curve

[deep hollow]

Translated:
The figure on the right shows the graph of a sine function f (x).

Determine the equation of f .

To do this, transfer the graph to your

sheet and draw in the quantities that are important for the calculation.

Problem :
my current problem is finding out what the the period is for the function c (i think its normaly called b our teacher just told us diffrent letters).
Because there is not shown an full period(from beginning back to beginning) i have great struggle. I would appreciate any help and we dont have to know x and c
i jsut need the period.

sorry for my poor english

[spring ledge]

The period is from top to top or bottom to bottom, and a half period is from bottom to top or top to bottom. You can find the half period then multiple it by to find the whole period

[spring ledge]

Also to find out what every step is you can say 6s=pi/2 where s is the number of steps then divide by 6 which becomes s=pi/12

[deep hollow]

i m lost tbh so i get that i could find the half of the period and multiple it to find the full, i also get that 1/2pi is 6 fields

now i dont understand how i should find the half

[deep hollow]

i m seasrching for the period lenght so i can divide 2pi through period lenght

but the problem i have is i cant figure out what the period lenght is because the repitition/period isnt shown completly

[deep hollow]

i understand that the period is from top to top, while the period lenght would be the distance between those two points

if i know the period lenght i could use the formel 2pi/b(period lenght) to get the period i want to place in my function

but in my picture it isnt shown fully

[spring ledge]

Ok find the half distance by finding the difference in x between top and bottom and to find the unit of every step assume from zero to the point is the amount of steps(squares) so 6s=pi/2 assuming s is the number of steps, then find value for 1 step after that find the x coordinates for both top on bottom by using the step info you found. Then find the difference in x between the top and bottom then multiple by 2 to get the whole distance

[deep hollow]

so i got the steps between bottom to top it is 10 steps

does that mean a full period has 20 steps?

[spring ledge]

Yes and one step is pi/12 like I we calculated before

[deep hollow]

and 20/6 would make 10/3 pi

so after that i can do 10/3or 3,33/2 and i would get the period i need

thank you very much i finaly understand it now

[spring ledge]

No 20*pi/12

[deep hollow]

so 20/12= 5/3pi after that 2pi divided by 5/3pi = 6/5

so my function now is f(x)= 3/5 · sinus(6/5 · x + c)+0,25

x and c is like i said not needed we only have to know what it stands for

[spring ledge]

How is it 0.25?

[deep hollow]

should be right or did i messed up something

[spring ledge]

I think the constent you added is wrong

[deep hollow]

class mate told me that it would be the intersection point of the graph and y axis

[deep hollow]

wdym?

[spring ledge]

But a sine function starts from the middle not the intersection

[deep hollow]

yeah i m not sure how to find out d do you know the formel or how i have to do it?

[spring ledge]

To find the middle point use (y2-y1)/2 to find the middle point add y1 again to find the coordinates of that point

[deep hollow]

isnt that amplitude ? the a at the ebginning before sinus

[spring ledge]

Yes the amplitude is the same as the distance from the top or bottom to midpoint but because you want to find the distance from the x axis add 0.2

[deep hollow]

and that would give me the y axis shift?

so like (1,4 - 0,2) divided by 2 = 3/5 + 0,2 ?

got it now (1,4 + 0,2) / 2

thank you very much for your help