A sinusoidal function has an amplitude of 5 units, a period of 120 degrees and a maximum at (0, 3). Represent the function with an equation in two different ways. what is the incorrect phase shift for cos?
The general equation for a sinusoidal function is given by:
y = A*sin(Bx + C) + D
where A represents the amplitude, B represents the frequency (in this case, the reciprocal of the period), C represents the phase shift, and D represents the vertical shift.
1st Representation:
Given that the amplitude is 5 units, the period is 120 degrees (or 2π/3 radians), and the maximum is at (0, 3), we can write the equation as:
y = 5*sin((2π/3)x + C) + 3
2nd Representation:
Since we know that the sine and cosine functions are shifted by 90 degrees (or π/2 radians), we can represent the function using the cosine function as well. In this case, the equation becomes:
y = 5*cos((2π/3)x + C) + 3
To find the incorrect phase shift for cosine, we need to consider that the cosine function is a shifted version of the sine function by 90 degrees. Therefore, the phase shift for cosine is always 90 degrees (or π/2 radians).