the functions f and g are given by f(θ) = 2 cos θ and g(θ) = 2 cos(bθ), where b is a constant. if the period…

the functions f and g are given by f(θ) = 2 cos θ and g(θ) = 2 cos(bθ), where b is a constant. if the period of g is half the period of f, then solving which of the following equations will give the correct value of b? a 2π/b = 1/2 b 2π/b = 1/2(2π) c 2π/b = 2π d 2π/b = 2(2π)

the functions f and g are given by f(θ) = 2 cos θ and g(θ) = 2 cos(bθ), where b is a constant. if the period of g is half the period of f, then solving which of the following equations will give the correct value of b? a 2π/b = 1/2 b 2π/b = 1/2(2π) c 2π/b = 2π d 2π/b = 2(2π)

Answer

Explanation:

Step1: Recall period formula for cosine

The period of $y = A\cos(kx)$ is $T=\frac{2\pi}{k}$. For $f(\theta)=2\cos\theta$, the period $T_f = 2\pi$. For $g(\theta)=2\cos(b\theta)$, the period $T_g=\frac{2\pi}{b}$.

Step2: Set up the relationship

Given that the period of $g$ is half the period of $f$. So, $\frac{2\pi}{b}=\frac{1}{2}(2\pi)$.

Answer:

B. $\frac{2\pi}{b}=\frac{1}{2}(2\pi)$