Calculate the amplitude, period, phase shifts, and 5 points for y=2-sin(2piex/3)
Amplitude = 2
Period = 3
phase shifts= 2pi/3
points:
1. x=0 y=2
2. x=1 y=1.13397
3. x=2 y=2.86603
4. x=3 y=2
5. x=4 y=1.13397
To calculate the amplitude, period, phase shifts, and 5 points for the given equation y = 2 - sin(2πex/3), let's break down each component step by step.
1. Amplitude:
The amplitude of a sine function is determined by the coefficient in front of the sin term. In this case, the coefficient is -1. Since the coefficient is negative, we need to consider the absolute value, which is 1. Therefore, the amplitude of this function is 1.
2. Period:
The period of a sine function is given by the formula 2π/b, where b is the coefficient of the x inside the sin function. In our case, the coefficient is 2πe/3. Therefore, the period of this function is 2π/(2πe/3) = 3/e.
3. Phase Shift:
The phase shift is determined by the constant term inside the sin function. In this case, there is no constant term, so the phase shift is 0.
4. 5 Points:
To find five points on the graph of the function, we can choose values for x and substitute them into the equation to get the corresponding y-values.
Let's choose five values of x and calculate the corresponding y:
When x = 0:
y = 2 - sin(2πe(0)/3)
y = 2 - sin(0)
y = 2
When x = π/2:
y = 2 - sin(2πe(π/2)/3)
y = 2 - sin(πe/3)
When x = π:
y = 2 - sin(2πe(π)/3)
y = 2 - sin(2πe/3)
When x = 3π/2:
y = 2 - sin(2πe(3π/2)/3)
y = 2 - sin(3πe/3)
y = 2 - sin(πe)
When x = 2π:
y = 2 - sin(2πe(2π)/3)
y = 2 - sin(4πe/3)
These five points will give you a good understanding of the shape and behavior of the given function.