Vector Analysis and Trigonometric Functions

The video tutorial explains how to determine the distance and direction a person must walk to return home after walking two miles west and four miles southwest. Using vector modeling, the tutorial calculates the resultant vector's magnitude and direction. The process involves breaking down the walk into vector components, summing them, and using trigonometry to find the angle needed to walk directly home. The final result provides the distance from home and the direction in degrees north of east.

What is the initial direction of the person's walk?

• North

• West

• East

• South

How is the southwest direction represented in terms of angle from the positive x-axis?

• 90 degrees

• 135 degrees

• 180 degrees

• 225 degrees

What is the x-component of the vector representing the walk southwest?

• 4

• -4

• 2

• -2

What is the y-component of the vector representing the walk southwest?

• -2

• 2

• 4

• -4

What is the formula used to find the magnitude of the resultant vector?

• Difference of components

• Sum of y-components

• Square root of the sum of squares of components

• Sum of x-components

Approximately how far is the person from home after the walk?

• 4.5 miles

• 3.5 miles

• 5.5 miles

• 6.5 miles

What trigonometric function is used to find the direction to head home?

• Sine

• Cotangent

• Cosine

• Tangent

In which quadrant is the angle theta located?

• First

• Second

• Third

• Fourth

What is the range of the inverse tangent function?

• 0 to 90 degrees

• -90 to 90 degrees

• 0 to 180 degrees

• -180 to 180 degrees

What is the final angle north of east for the person to head directly home?

• 15.36 degrees

• 30.36 degrees

• 60.36 degrees

• 45.36 degrees