Height and Cosine Function Analysis

The video tutorial addresses a trigonometric problem involving Joy's running path on a 2π km stretch of rolling hills. The height of the hills above sea level is modeled by the function h(D) = 4cos²D - 1. The tutorial explains how to determine the intervals where the height is above sea level by solving the inequality and finding zero points. It includes a graphical representation to visualize the function and concludes with identifying the intervals where the height is greater than zero.

What is the main problem discussed in the video?

• Determining the speed of Joy.

• Finding the maximum height of the hills.

• Calculating the total distance Joy runs.

• Finding the intervals where the height is above sea level.

What is the function used to model the height of the hills?

• h(D) = 4 tan² D - 1

• h(D) = 2 cos D - 1

• h(D) = 4 cos² D - 1

• h(D) = 4 sin² D - 1

What is the domain of the problem?

• D is between 0 and pi

• D is between 0 and 4 pi

• D is between 0 and 2 pi

• D is between 0 and 2

What is the first step in solving the inequality?

• Finding when the height is maximum

• Finding when the height is minimum

• Finding when the height is constant

• Finding when the height is zero

What is the value of cos D when the height is zero?

• cos D = ±1/4

• cos D = ±1/2

• cos D = 1

• cos D = 0

What special triangle is used to find when cos D is half?

• 30-30-120 triangle

• 60-60-60 triangle

• 30-60-90 triangle

• 45-45-90 triangle

At what angles is the height zero?

• 0°, 180°, 360°

• 45°, 135°, 225°, 315°

• 60°, 120°, 240°, 300°

• 30°, 90°, 180°, 270°

What happens to the cosine function when squared?

• Values remain unchanged

• Values double

• All values become negative

• All values become positive

In which intervals is the height above sea level?

• 30° to 150°, 210° to 330°

• 60° to 120°, 240° to 300°

• 0° to 90°, 180° to 270°

• 0° to 60°, 120° to 240°, 300° to 360°

What is the significance of the intervals found?

• They indicate when the height is at sea level

• They indicate when the height is constant

• They indicate when the height is above sea level

• They indicate when the height is below sea level