Vector Components and Trigonometric Values

The video tutorial explains how to find the components of a vector using its magnitude and angle. It starts by placing the vector on a coordinate plane, identifying its position in the second quadrant. The tutorial then demonstrates how to calculate the vector's x and y components using trigonometric functions, specifically cosine and sine. It uses a reference triangle and the unit circle to find these values. The process of scalar multiplication and simplification is also covered, resulting in the vector's component form. The tutorial concludes by verifying the trigonometric values using the unit circle.

What is the initial point of vector C assumed to be?

• At the origin on the coordinate plane

• At point (1,1)

• At the end of the vector

• At point (0,1)

In which quadrant is vector C located?

• Second quadrant

• First quadrant

• Fourth quadrant

• Third quadrant

What is the formula for the X component of a vector with angle Theta?

• Magnitude divided by sine Theta

• Magnitude divided by cosine Theta

• Magnitude times cosine Theta

• Magnitude times sine Theta

What is the positive angle Theta used for vector C?

• 180°

• 60°

• 90°

• 120°

What type of triangle is used as a reference for finding trigonometric values?

• 45-45-90 triangle

• 30-60-90 triangle

• Isosceles triangle

• Equilateral triangle

What is the cosine of 120° using the reference triangle?

• √3/2

• -1/2

• -√3/2

• 1/2

What is the sine of 120° using the reference triangle?

• -1/2

• -√3/2

• √3/2

• 1/2

What is the X component of vector C after scalar multiplication?

• 9

• 18

• -18

• -9

What is the Y component of vector C after scalar multiplication?

• -9√3

• -9

• 9√3

• 9

How can the trigonometric values be verified?

• Using a calculator

• Using the unit circle

• Using a ruler

• Using a protractor