Final answer:
Using the equation y = 3.06sin(0.017x - 1.40) + 12.23, if y = 15, then the value of x is approximately 3961.76.
Step-by-step explanation:
To solve the equation y = 3.06sin(0.017x - 1.40) + 12.23, we need to find the values of x that satisfy the equation.
1. First, let's isolate the sine term on one side of the equation:
y - 12.23 = 3.06sin(0.017x - 1.40)
2. Next, divide both sides of the equation by 3.06 to isolate the sine term:
(y - 12.23) / 3.06 = sin(0.017x - 1.40)
3. Now, we need to find the inverse of the sine function to get the angle. Let's call the inverse sine function arcsin:
arcsin((y - 12.23) / 3.06) = 0.017x - 1.40
4. To isolate x, we need to undo the operations on the right side of the equation. First, add 1.40 to both sides:
arcsin((y - 12.23) / 3.06) + 1.40 = 0.017x
5. Finally, divide both sides by 0.017 to solve for x:
x = (arcsin((y - 12.23) / 3.06) + 1.40) / 0.017
Now, you can substitute different values of y into this equation to find the corresponding x-values. For example, if y = 15, you can calculate x as follows:
x = (arcsin((15 - 12.23) / 3.06) + 1.40) / 0.017
x= approximately 3961.76.