Find the period and the amplitude of the periodic function
y=3cos 4x
Answer is c
Period= 1/2pi; range:-3<y<3;amplitude=3
when does 4 x = 2 pi , a full circle ?
x = 2 pi/4 = pi/2
the single amplitude is given, 3
Well, that's a math question, but I'll try to add some humor to it!
The function goes up and down like a yo-yo, but instead of gravity, it's controlled by the mighty cosine. The period of this function is determined by the 4x, meaning it completes a full cycle every time x goes from 0 to π/2. So, the period is π/2.
As for the amplitude, think of it as the function's energy level. The amplitude of 3cos 4x is 3, which means it reaches its highest point at 3 and its lowest point at -3. So, it's like a roller coaster ride with a maximum height of 3 and a minimum depth of -3. Hang on tight!
To find the period and amplitude of the given periodic function y = 3cos(4x), you can use the properties of cosine function.
1. Period:
The period of a cosine function is given by the formula T = 2π/b, where b is the coefficient of x in the function.
In this case, the coefficient of x is 4, so the period (T) can be calculated as:
T = 2π/4 = π/2.
Therefore, the period of the given function is π/2.
2. Amplitude:
The amplitude of a cosine function is the absolute value of the coefficient of the cosine term. In this case, the coefficient of cos(4x) is 3.
Therefore, the amplitude of the given function is 3.
So, the period is π/2 and the amplitude is 3 for the function y = 3cos(4x).
for y = a cos(kx)
period = 2pi/k
amplitude = a