What are the period and amplitude of the function y=2sin4 theta?
A. pi/2 and 2
B. pi and 4
C. pi/2 and 4
D. pi/2 and 1
I think the answer is A. Am i correct?
amplitude is 2
when theta = pi/2 we have sin 2 pi
so period is pi/2
A.
Well, let me put on my imaginary mathematician wig and check the situation for you, my friend.
According to the equation given, y = 2sin(4θ), we can see that the coefficient inside the sine function is 4. This means that the value of θ is being multiplied by 4, which, in turn, affects the period of the function.
The period of a sine function is usually 2π divided by the coefficient of θ. So in this case, the period would be 2π/4, which simplifies to π/2.
As for the amplitude, it doesn't depend on the coefficient of the angle variable. The amplitude is always the absolute value of the coefficient in front of the sine function. In this case, the amplitude is 2.
So, after all the calculations and clowning around, the correct answer would be C: π/2 and 4. Keep up the good work, my friend!
To find the period and amplitude of the given function y = 2sin(4θ), we can use the standard form of a sine function: y = A*sin(Bθ + C) + D.
In this case, A = 2, which represents the amplitude. The amplitude is the absolute value of the vertical distance between the maximum and minimum values of the function, so the amplitude is 2.
The B value in the standard form represents the coefficient of θ inside the sine function. In this case, B = 4. The period, P, of a sine function with coefficient B is given by P = 2π/B. So, the period of the function y = 2sin(4θ) is 2π/4 = π/2.
Therefore, the correct answer is option C, π/2 and 4.
To determine the period and amplitude of the function y = 2sin(4θ), we can use some properties of the sine function.
The general form of a sine function is y = A*sin(Bθ + C), where A represents the amplitude, B represents the frequency or number of cycles in the interval [0, 2π], and C represents any phase shift.
In this specific case, the equation y = 2sin(4θ) has an amplitude of 2. The amplitude describes the maximum value the function reaches above and below its average value.
To find the period, we need to determine the value of B in the general form of the sine function. In our case, B = 4, which means the function completes four cycles in the interval [0, 2π]. The period is the distance between corresponding points on the graph of the function, and it is given by the formula T = 2π/B.
So, the period of the function y = 2sin(4θ) is T = 2π/4 = π/2.
Therefore, the correct answer is option C: π/2 and 4.