Find the equation of a sine function that has a vertical displacement 2 units down, a horizontal phase shift 60 degrees to the right, a period of 30 degrees, a reflection in the y-axis and an amplitude of 3.
My attempt at an answer:
Y = 3 sin (30x- 60) -2
Can someone tell me if this is correct?
To verify if your equation is correct, let's go through each of the given characteristics and compare them with the equation you provided:
1. Vertical displacement 2 units down:
In the equation Y = 3 sin (30x - 60) - 2, the -2 term indicates a vertical displacement 2 units down, which is correct.
2. Horizontal phase shift 60 degrees to the right:
In the equation Y = 3 sin (30x - 60) - 2, the term inside the sine function, 30x - 60, indicates a horizontal phase shift 60 degrees to the right. This is also correct.
3. Period of 30 degrees:
The period of a sine function is typically denoted as 2π/b, where b represents the coefficient of x inside the sine function. In this case, the coefficient is 30, so the period would be 2π/30, which equals 1/15. This means that the function repeats itself every 1/15 of a full cycle, which is equivalent to 24 degrees, not 30 degrees. Therefore, the period in your equation is not accurate.
4. Reflection in the y-axis:
A reflection in the y-axis would indicate a negative sign in front of the sine function. However, in your equation, the sine function is not negated.
5. Amplitude of 3:
In the equation Y = 3 sin (30x - 60) - 2, the coefficient 3 in front of the sine function represents the amplitude, which is correct.
Based on the analysis above, your equation is mostly correct, but the period and the reflection in the y-axis are not accurately represented. Here is the corrected equation:
Y = -3 sin (2π/30 * (x - 60)) - 2
Please note that the period is now correctly calculated as 2π/30, which is equivalent to 24 degrees. Additionally, the negative sign in front of the sine function represents the reflection in the y-axis.