Question

I'm really struggling with this right now. i know how to solve for everything but c and i can't find any help anywhere :( i just need help with finding c but feel free to explain the entire thing for others
g is a trigonometric function of the for g(x)=acos(bx+c)+d

below is the graph of g(x). the function has a maximum point at (2,11) and a minimum point at (3.5,1).

find a formula for g(x). give an exact expression.

Answer 1

Answer:

$g(x) = 5 \cos(\frac23 \pi x + \frac23 \pi)+6$

Step-by-step explanation:

Let's start with the simple ones:

a = amplitude = (highest - lowest) divided by 2 = (11-1)/2 = 5

d = offset = (highest + lowest) divided by 2 = (11+1)/2 = 6

Now, if x goes 'untreated', the cos would make a full swing after 2pi.

Here, it repeats after 3. To achieve that, we divide by 3 and multiply by 2pi.

b = 2pi/3

You can try it out (assuming c=0 for a minute): x=3 puts bx at 2pi.

Now for the final one, the shift left by one. We cannot say c=1 because that would be a 1 on the 2pi scale.

Rather, the shift would be c'=1 if the formula were acos(b(x+c')).

If we work out the parenthesis with c'=1, we get bx + b, so the actual c is 2pi/3

Answer 2

Answer:

a = amplitude = (highest - lowest) divided by 2 = (11-1)/2 = 5

d = offset = (highest + lowest) divided by 2 = (11+1)/2 = 6

   we divide by 3 and multiply by 2pi.

b = 2pi/3

Hope I can help you :)