Find the period and amplitude of the following function. Then sketch the function from 0 to 2π.
y = -2 sin 2π0
show your work
The given function is y = -2 sin 2π0.
To find the period of the function, we can use the formula for the period of a sine function, which is 2π/b, where b is the coefficient of the angle. In this case, b = 2π0 = 0.
So, the period of the function is 2π/0, which is undefined. Therefore, the function does not repeat itself and does not have a period.
To find the amplitude of the function, we look at the coefficient of the sine function. In this case, the coefficient is -2.
So, the amplitude of the function is 2.
Now let's sketch the function from 0 to 2π:
Since the coefficient of the angle is 0, the function can be written as y = -2 sin(0), which simplifies to y = 0.
The graph of y = 0 is a straight line that intersects the x-axis at y = 0 for all values of x.
Therefore, the graph of y = -2 sin 2π0 is a straight line with a constant value of -2, which does not change with any value of x from 0 to 2π.