Question

The height H in feet, above the ground of the bob of a pendulum can be modeled by H(θ) = 6cosθ + 10, where θ is the angle that the pendulum makes with a vertical extended to the ground. Identify the graph that represents the height of the bob for 0° ≤ θ ≤ 180°.

PLS HELP

Answer 1

The graph of H(θ) = 6cosθ + 10 is a sinusoidal function. The period of a sinusoidal function is the distance between two consecutive points where the function repeats itself. The period of H(θ) = 6cosθ + 10 is 360°. Since 0° ≤ θ ≤ 180°, the graph of H(θ) = 6cosθ + 10 will repeat itself once between 0° and 180°. This means that the graph will start at a maximum height of 16, reach a minimum height of 4, reach a maximum height of 16 again, and then reach a minimum height of 4 again. The graph of H(θ) = 6cosθ + 10 will also pass through the origin once.