chapter 6 quiz\n170 points possible answered: 0/17\nquestion 1\nsolve 4 cos(4x) = 2 for the smallest…

Explanation:

Step1: Isolate the cosine function

Divide both sides of the equation (4\cos(4x) = 2) by (4). (\cos(4x)=\frac{2}{4}=\frac{1}{2})

Step2: Solve for (4x)

We know that if (\cos\theta=\frac{1}{2}), then (\theta = 2n\pi\pm\frac{\pi}{3}), (n\in\mathbb{Z}). For the smallest positive solution, we take (n = 0) and the positive case (\theta=4x=\frac{\pi}{3}) (since (\cos\frac{\pi}{3}=\frac{1}{2}) and we want the smallest positive input to the cosine function).

Step3: Solve for (x)

Divide both sides of (4x=\frac{\pi}{3}) by (4). (x=\frac{\pi}{12}) Now, calculate (\frac{\pi}{12}\approx\frac{3.14159}{12}\approx0.26)

Answer:

(0.26)