In the values interval [0, 2p] the function f (x) = sin(x) has more periods by the function g (x) = sin(3x).
True or False?
false.
sin(3x) oscillates 3 times as fast as sin(x)
Thank you Steve!!!
To determine whether the function f(x) = sin(x) has more periods than the function g(x) = sin(3x) in the interval [0, 2π], we need to compare the periods of each function.
The period of f(x) = sin(x) is equal to 2π. This means that the graph of f(x) repeats itself every 2π units.
The period of g(x) = sin(3x) can be found by taking the period of sin(x) and dividing it by the coefficient in front of x, which is 3. Therefore, the period of g(x) is 2π/3.
Now, we can compare the periods: 2π (f(x)) vs. 2π/3 (g(x)).
Since 2π/3 is smaller than 2π, this means that g(x) = sin(3x) actually has more periods within the interval [0, 2π]. Therefore, the statement "In the values interval [0, 2π], the function f(x) = sin(x) has more periods than the function g(x) = sin(3x)" is False.