Vector Components and Trigonometric Functions

The video tutorial explains how to find the components of a vector using its magnitude and direction. It starts by assuming the vector's initial point is at the origin and lies along the negative x-axis. The tutorial then introduces the use of trigonometry, specifically cosine and sine functions, to determine the vector's components. By considering the angle of 180 degrees, the tutorial demonstrates how to calculate the x and y components of the vector, confirming the results through different methods.

What is the initial point of a vector assumed to be when finding its components on a coordinate plane?

• At the origin

• At the terminal point

• At any random point

• At the midpoint

If a vector lies along the negative x-axis and has a magnitude of 39, what is its terminal point?

• (0, 39)

• (-39, 0)

• (0, -39)

• (39, 0)

How can you find the x component of a vector with a known magnitude and angle?

• Magnitude times cosine of the angle

• Magnitude divided by cosine of the angle

• Magnitude times sine of the angle

• Magnitude divided by sine of the angle

What angle is most obvious to use for a vector lying along the negative x-axis?

• 90 degrees

• 270 degrees

• 0 degrees

• 180 degrees

What is the cosine of 180 degrees?

• 1

• 0

• -1

• 0.5

What is the sine of 180 degrees?

• 1

• 0

• -1

• 0.5

How can you verify the trigonometric values of angles using the unit circle?

• By checking the intersection points

• By measuring the radius

• By calculating the area

• By finding the circumference

What is the x component of vector b if its magnitude is 39 and it lies along the negative x-axis?

• 1

• 0

• -39

• 39

What is the y component of vector b if it lies along the negative x-axis?

• 1

• 0

• -39

• 39

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

• Tangent

• Cosine

• Secant

• Sine