an electric current I , in amps is given by:
I= cos(wt) + sqrt of 3 sin(wt)
where w is positive constant. what are the max and minimum values of I?
To find the maximum and minimum values of the given current equation, we need to identify the maximum and minimum values of the cosine and sine functions separately.
Let's first consider the maximum and minimum values of the cosine function:
The maximum value of the cosine function is 1.
The minimum value of the cosine function is -1.
Next, let's find the maximum and minimum values of the sine function:
The maximum value of the sine function is 1.
The minimum value of the sine function is -1.
Now, in the given current equation, I = cos(wt) + sqrt(3)sin(wt).
To find the maximum and minimum values of I, we substitute the maximum and minimum values of the cosine and sine functions into the equation.
For the maximum value of I:
I_max = cos(wt) + sqrt(3)sin(wt) = 1 + sqrt(3)(1) = 1 + sqrt(3)
For the minimum value of I:
I_min = cos(wt) + sqrt(3)sin(wt) = -1 + sqrt(3)(-1) = -1 - sqrt(3)
Therefore, the maximum value of the current is 1 + sqrt(3) amps, and the minimum value is -1 - sqrt(3) amps.
To find the maximum and minimum values of the electric current I, we need to consider the amplitude of the cosine and sine functions.
The general form of cosine and sine functions can be written as:
cos(x) = A cos(wt)
sin(x) = B sin(wt)
where A is the amplitude of the cosine function, and B is the amplitude of the sine function.
In the given equation:
I = cos(wt) + sqrt(3) sin(wt)
we can see that the amplitude of the cosine function is 1, and the amplitude of the sine function is √3.
Therefore, the maximum value of I will be the sum of these two amplitudes, which is 1 + √3.
The minimum value of I will be the negative sum of these two amplitudes, which is -(1 + √3).
So, the max value of I is 1 + √3, and the min value of I is -(1 + √3).