Vector Components and Trigonometric Functions

The video tutorial explains how to find the component form of a vector given its magnitude and direction. It begins by sketching the vector on a coordinate plane, identifying its position in the third quadrant, and calculating the angle it makes with the negative x-axis. The tutorial then uses trigonometry to determine the x and y components of the vector, providing exact values using both a reference triangle and the unit circle. The process involves calculating cosine and sine values for the given angle, ensuring the components are accurately determined.

What is the magnitude of vector v?

• 6

• 7

• 5

• 8

In which quadrant does vector v lie?

• First

• Second

• Third

• Fourth

What is the angle theta for vector v in standard position?

• 210 degrees

• 270 degrees

• 240 degrees

• 180 degrees

What forms when the x and y components of vector v are sketched?

• A right triangle

• A rectangle

• A circle

• A square

What is the cosine of 210 degrees?

• -1/2

• 1/2

• -sqrt(3)/2

• sqrt(3)/2

What is the sine of 210 degrees?

• -sqrt(3)/2

• 1/2

• -1/2

• sqrt(3)/2

How is the x component of vector v calculated?

• 7 * sin(210 degrees)

• 7 * cos(210 degrees)

• 7 * cot(210 degrees)

• 7 * tan(210 degrees)

How is the y component of vector v calculated?

• 7 * cos(210 degrees)

• 7 * cot(210 degrees)

• 7 * tan(210 degrees)

• 7 * sin(210 degrees)

What is the exact x component of vector v?

• -7/2

• -7sqrt(3)/2

• 7sqrt(3)/2

• 7/2

What is the exact y component of vector v?

• -7/2

• -7sqrt(3)/2

• 7sqrt(3)/2

• 7/2