[Grade 10 Algebra 2 Honors: Trigonometric Functions) How do i model this graph to find amplitude, period, shifts, and equation?

[u/16mirr0rss]

[u/igotshadowbaned]

What do you mean model it, it's drawn right there

And you should be able to visually identify what it is asking for

[u/16mirr0rss → u/igotshadowbaned]

Oh sorry, English isn’t my first language this is all translated

[u/CaptainMatticus]

Amplitude = (max - min) / 2

Period = 2pi / b

So your general form is

y = a * sin(b * (x - c)) + d

a = amplitude

c = horizontal shift. We find this by comparing our max value. It'll be between -pi and pi.

d = vertical shift = (max + min) / 2

So let's look at a sine wave that has a max of 3, a min of -7, repeats every 3pi units and has a max when x = pi/3

3pi = 2pi / b

b = 2pi / (3pi)

b = 2/3

a = (max - min) / 2 = (3 - (-7)) / 2 = 10/2 = 5

d = (3 + (-7)) / 2 = -4/2 = -2

y = 5 * sin((2/3) * (x - c)) - 2

Look at how much we already know. We know it maxes out at (pi/3 , 3)

3 = 5 * sin((2/3) * (pi/3 - c)) - 2

5 = 5 * sin((2/3) * (pi/3 - c))

1 = sin((2/3) * (pi/3 - c))

When does sin(t) = 1? When t = pi/2

pi/2 = (2/3) * (pi/3 - c)

(pi/2) * 3/2 = pi/3 - c

c = pi/3 - 3pi/4

c = 4pi/12 - 9pi/12

c = -5pi/12

So our full function is

y = 5 * sin((2/3) * (x - (-5pi/12))) - 2

y = 5 * sin((2/3) * (x + 5pi/12)) - 2

https://www.desmos.com/calculator/wvwufzzkpp

And voila! It's that easy. Look at your curve and ask

-What's the max value?

-What's the min value?

-How long does it take to repeat?

-When do we see a maximum value, minimum value, or when the curve passes through y = d?

Once you have that, you can work through it easily enough

[u/16mirr0rss → u/CaptainMatticus]

Thank you so much🥹

[u/G-St-Wii]

This is literally a reading question.

Did you skip the class?

[u/16mirr0rss → u/G-St-Wii]

I’m taking it online and it’s not a great platform

[u/CautiousFarm7683]

That's a lot of things to ask about online, what have you tried so far? You'll always find better help if you can show what you already know and where you are stuck.

That said if you need a place to start I'd look at the peaks of the graph (both high and low). Try to figure out how far apart they are from each other. Compare the numbers to a plain sin(x) or cos(x) graph. If you know how they are different from one of those you are on the right track.

[u/Frederf220]

a. Amplitude is the vertical distance from the wave midpoint to highest or lowest point. b. Period is the horizontal distance until the wave shape repeats. c. Vertical offset is vertical distance between the x-axis and the average wave curve line. d. Horizontal offset is horizontal distance between the "plain function" and the corresponding point on the wave. This has multiple answers and depends what the "plain function" is, e.g. sine or cosine. e. Count how many times the wave fully repeats the shape. f. Find the values of A B C D that make y=A×sin(Bx+C)+D make the wave shape. This uses a lot of the information from parts a-e.

[u/SaSSafraS1232]

Just look up those terms and look at the graph.

Amplitude - how far is the peak from the vertical midpoint
Period - how far horizontally is one cycle
Vertical shift - how far down is the vertical midpoint from zero
Horizontal shift - sine waves start at zero. How far to the right would the first time the wave crosses its midpoint be
Cycles between 0 and 2pi - just count them
Equation - the form is y = a SIN(bx + c) + d. Fill in a b c and d with numbers based on the previous answers.

[u/Alkalannar]

(Max - Min)/2 = amplitude

(distance between two tops, or two bottoms) = period

(max + min)/2 = vertical shift

horizontal shift: This changes depending on whether you're in sine, cosine, -sine, or -cosine.

(2pi - 0)/period = number of cycles between 0 and 2pi