How do you find the value of m in the equation y=k+asin(mx)?

sorry my response is so late...

I tried solving it again and I got the equation y=2+4sin(3x). I got the two because the graph is shifted 2 units up and I got the four from the graph being stretched vertically 4 times. Then I plugged in the point (30,6) into the equation y=2+4sin(mx) and I got that m was 3(?). Is this right? I'm not sure...

y=k+asin(mx)

asin(mx) = y-k
sin(mx) = (y-k)/a
mx = arcsin( (y-k)/a )
m = (1/x)( arcsin( (y-k)/a ) ) or (1/x)( sin^-1 ( (y-k)/a ) )

what if you had a maximum point let's say (30,6) and a y-int of (2,0) and you had to find the equation of the graph? I get how to find the other variables just not m.

Ahhh, so that was the original question, ok ....

go back to your original:
y = k+asin(mx)
y' = acos(mx)*m = 0 for a max
amcos(mx) = 0
am = 0 or cos(mx) = 0 , forget about the am=0

cos(mx) = 0 , but x = 30 from the max of (30,6)
cos 30m = 0
30m = π/2
m = π/60
sub (30,6) into original
6 = k + asin((π/60)(30) )
6 = k + a sin π/2
6 = k + a(1) ----> a + k = 6 **

also (2,0) lies on it.
0 = k + a sin( 2π/60)
0 = k + asin π/30 --- k + .104528..a = 0 ***
subtract *** from **
.89547a = 6
a = appr 6.7
k = 6 - a = appr .7

so y = .7 + 6.7 sin((π/60)x) , check my work

To find the value of m in the equation y = k + a*sin(mx), you need to have more information. Specifically, you need to know the value of y at a particular point or a set of points, and the corresponding values for x. With this information, you can solve the equation for m.

Here are the steps to find the value of m:

1. Choose a point (x, y) on the graph. If you have multiple points, choose one that is relatively easy to work with.
2. Plug in the values of x and y into the equation. You will get an equation in terms of m.
3. Rearrange the equation to isolate the variable m. This may involve algebraic manipulation and possibly some trigonometric identities.
4. Solve the equation for m using algebraic techniques. This could include factoring, isolating the variable, or using logarithms if necessary.
5. Once you have found the value of m, you can substitute it back into the original equation to find the value of y at other points or to verify the solution.

It is important to note that without specific values for y and x, it is not possible to determine the exact value of m. However, by following the steps outlined above, you can solve for m given specific values for y and x.

If BE−→−BE→ bisects ∠ABD and m∠ABD = 66°, find m∠ABE.