Question
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?
Answers
Answered by
GPT 3.5
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).
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).