Identify the amplitude and period of the following functions.
$g\left(\theta\right)=3\cos\left(\frac{\theta}{3}\right)$

Verified step by step guidance

1. The given function is g(θ) = 3cos(θ/3). This is a cosine function of the form a * cos(bθ), where a is the amplitude and b affects the period.
2. Identify the amplitude: In the function g(θ) = 3cos(θ/3), the coefficient of the cosine function is 3. Therefore, the amplitude is the absolute value of this coefficient, which is |3| = 3.
3. Determine the period: The period of a basic cosine function cos(θ) is 2π. For a function of the form cos(bθ), the period is adjusted by the factor b, and is given by the formula 2π/|b|.
4. In the function g(θ) = 3cos(θ/3), the value of b is 1/3 (since θ/3 can be rewritten as (1/3)θ). Therefore, the period is 2π divided by 1/3, which simplifies to 2π * 3.
5. Thus, the amplitude of the function is 3, and the period is 6π.