Understanding Vector Components

The video tutorial explains how to determine the x and y components of a vector given its magnitude and angle with the positive x-axis. It uses right triangle trigonometry to derive the formulas for these components, demonstrating the process with an example vector of magnitude 8 and a 60-degree angle. The tutorial evaluates trigonometric functions to find the components and concludes with a simplified method for future calculations.

What is the x component of a vector in terms of its magnitude and angle with the x-axis?

• Magnitude times cosine of the angle

• Magnitude divided by sine of the angle

• Magnitude times sine of the angle

• Magnitude divided by cosine of the angle

In the example, what is the magnitude of the vector used?

• 8 units

• 10 units

• 5 units

• 6 units

What is the relationship between cosine theta and the sides of a right triangle?

• Adjacent side divided by hypotenuse

• Hypotenuse divided by opposite side

• Hypotenuse divided by adjacent side

• Opposite side divided by hypotenuse

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

• Divide the magnitude by sine of the angle

• Divide the magnitude by cosine of the angle

• Multiply the magnitude by sine of the angle

• Multiply the magnitude by cosine of the angle

What is the value of cosine 60 degrees?

• √3/2

• 0

• 1

• 1/2

What is the value of sine 60 degrees?

• 1

• 1/2

• √3/2

• 0

What is the x component of the vector in the example after simplification?

• 2

• 3

• 4

• 5

What is the y component of the vector in the example after simplification?

• 3√3

• √3

• 4√3

• 2√3

Which trigonometric function is used to find the horizontal component of a vector?

• Tangent

• Cotangent

• Cosine

• Sine

Which trigonometric function is used to find the vertical component of a vector?

• Tangent

• Cosine

• Sine

• Cotangent