Trigonometric Functions and Vectors

The video tutorial explains how to find the component form of a vector with a given magnitude and angle. It starts by identifying the vector's position in Quadrant 3 and calculating the angle from the negative Y-axis. Using trigonometric functions, the tutorial demonstrates how to determine the vector's X and Y components, ensuring exact values are obtained. Finally, the vector is expressed in component form, highlighting the negative values due to its position in Quadrant 3.

What is the magnitude of the vector we are analyzing?

• 2

• √5

• 2√5

• 5

In which quadrant does the vector lie?

• Quadrant 4

• Quadrant 3

• Quadrant 1

• Quadrant 2

What is the angle between the vector and the negative Y-axis?

• 120 degrees

• 30 degrees

• 60 degrees

• 90 degrees

What is the angle of the vector in standard position?

• 300 degrees

• 270 degrees

• 240 degrees

• 210 degrees

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

• Tangent

• Cotangent

• Sine

• Cosine

What is the cosine of 240 degrees?

• 1/2

• -1/2

• √3/2

• -√3/2

What is the X component of the vector?

• √15

• -√5

• √5

• -√15

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

• Sine

• Cosine

• Secant

• Tangent

What is the sine of 240 degrees?

• √3/2

• -1/2

• 1/2

• -√3/2

What is the Y component of the vector?

• √5

• -√5

• √15

• -√15