Question

What is the period of f(x)=cos(2x)sin(4x)?

a) π/3
b) π/2
c) 2π/3
d) π
e) 2π

Answer 1

The period of the function f(x) = cos(2x)sin(4x) is determined by the least common multiple of the periods of cos(2x) and sin(4x), which is π.

Step-by-step explanation:

The period of the function f(x) = cos(2x)sin(4x) can be found by examining the components cos(2x) and sin(4x) separately. The period of the cosine function is the length of one complete cycle of the graph. For cos(2x), this period is π because the usual period of the cosine function, which is 2π, is divided by the coefficient of x, which is 2. Similarly, for sin(4x), the period is π/2, as the usual period 2π is divided by 4. The period of the combined function f(x) = cos(2x)sin(4x) is the least common multiple (LCM) of the individual periods, which is π. So, the correct answer is d) π.