state the smallest interval for 5 sin theta to produce a complete graph.
To find the smallest interval for the function 5sin(θ) to produce a complete graph, we need to consider the period of the sine function.
The general formula for the period of the sine function is given as:
Period (T) = 2π/|B|
In this case, the coefficient in front of sin(θ) is 5, and according to the formula, the period is given by:
T = 2π/5
To find the smallest interval for a complete graph, we need to find the value of θ that completes one full cycle of the sine function. Since one full cycle occurs when θ increases by 2π, we can calculate the smallest interval as:
Interval = T = 2π/5
Therefore, the smallest interval for the function 5sin(θ) to produce a complete graph is 2π/5.
To determine the smallest interval for 5 sin(theta) to produce a complete graph, let's first understand the properties of the sine function.
The sine function, sin(theta), is a periodic function with a period of 2π. This means that the graph of sin(theta) repeats itself every 2π units.
To find the smallest interval for 5 sin(theta) to produce a complete graph, we need to divide the period of sin(theta) by the coefficient of theta, which is 5 in this case.
So, the period of the function 5 sin(theta) is given by:
Period = 2π / |5|
Since the coefficient 5 is positive, we take the absolute value to ensure a positive result.
Now, calculating the period:
Period = 2π / 5
Therefore, the smallest interval for 5 sin(theta) to produce a complete graph is 2π/5.