Vector Components and Trigonometry

The video tutorial explains how to express vectors in component form using trigonometry. It begins by introducing the concept of vector components and sketching vectors on a coordinate plane. The tutorial then demonstrates how to use trigonometric functions, such as cosine and sine, to calculate the horizontal and vertical components of a vector. It provides examples with different angles and discusses the formulas used to simplify the process. The video concludes with a practical example of finding vector components for a vector with a 135° angle.

What is the initial point of a vector in component form?

• The endpoint

• The midpoint

• The origin

• The terminal point

Which angle is used to determine the direction of a vector on a coordinate plane?

• The angle between the vector and the origin

• The angle between the vector and the y-axis

• The angle between the vector and the z-axis

• The angle between the vector and the x-axis

How do you calculate the horizontal component of a vector using trigonometry?

• Multiply the magnitude by cosine of the angle

• Divide the magnitude by cosine of the angle

• Add the magnitude to cosine of the angle

• Multiply the magnitude by sine of the angle

What is the formula for the vertical component of a vector?

• Magnitude divided by sine of the angle

• Magnitude times cosine of the angle

• Magnitude times sine of the angle

• Magnitude plus sine of the angle

In a 30°-60°-90° triangle, what is the cosine of 30°?

• √2/2

• 1/2

• √3/2

• 1/√3

What is the component form of a vector with a magnitude of 8 and a direction of 30°?

• (4, 4√3)

• (0, 8)

• (8, 0)

• (4√3, 4)

How do you find the component form of a vector using its magnitude and direction?

• By adding the magnitude to the direction

• By multiplying the magnitude by the direction

• By using trigonometric functions with the magnitude and direction

• By dividing the magnitude by the direction

What is the reference angle for a vector with a direction of 135°?

• 45°

• 90°

• 60°

• 30°

In which quadrant is a vector with a direction of 135° located?

• Fourth quadrant

• Third quadrant

• First quadrant

• Second quadrant

What is the component form of a vector with a magnitude of 14 and a direction of 135°?

• (0, 14)

• (14, 0)

• (7√2, -7√2)

• (-7√2, 7√2)