Question

Solve 4cos(4x)=2

for the smallest three positive solutions.

Give your answers accurate to at least two decimal places, as a list separated by commas.

Answer 1

Starting with the given equation:
4cos(4x) = 2

Dividing both sides by 4:
cos(4x) = 1/2

Using the inverse cosine function, we find the angles where cos(4x) = 1/2:
4x = ±π/3 + 2πn, where n is an integer
x = ±π/12 + (π/2)n, where n is an integer

To find the smallest three positive solutions, we need to start with n = 0 and find the first three positive solutions:
x = π/12, 7π/12, and 13π/12

Rounding to two decimal places, the smallest three positive solutions are:
x = 0.26, 0.61, and 1.08

Therefore, the solutions are 0.26, 0.61, and 1.08, separated by commas.