Vector Components and Trigonometry

The video tutorial explains how to find the component form of a vector given its magnitude and angle with the positive x-axis. It involves sketching the vector in standard position, identifying its quadrant, and calculating the x and y components using trigonometric functions. The tutorial also demonstrates using a calculator to find approximate values for these components, ensuring the calculator is in degree mode. The final component values are rounded to two decimal places, and the tutorial concludes by verifying the results with the vector's position in the third quadrant.

What is the magnitude of vector v?

• 48

• 36

• 24

• 12

In which quadrant does the vector lie if it makes a 245.7-degree angle with the positive x-axis?

• Fourth

• Third

• Second

• First

Why are both the x and y components of the vector negative?

• Because the vector is in the first quadrant

• Because the vector is in the second quadrant

• Because the vector is in the third quadrant

• Because the vector is in the fourth quadrant

What is the formula for the x component of a vector given its magnitude and angle?

• Magnitude divided by sine of the angle

• Magnitude times cosine of the angle

• Magnitude times sine of the angle

• Magnitude divided by cosine of the angle

What is the formula for the y component of a vector given its magnitude and angle?

• Magnitude divided by cosine of the angle

• Magnitude divided by sine of the angle

• Magnitude times cosine of the angle

• Magnitude times sine of the angle

What is the approximate value of the x component of the vector?

• -9.88

• -21.87

• 21.87

• 9.88

What should you ensure about your calculator before calculating trigonometric values?

• It is in standard mode

• It is in degree mode

• It is in radian mode

• It is in scientific mode

What is the approximate value of the y component of the vector?

• 21.87

• -9.88

• -21.87

• 9.88

Why do we use an approximation symbol for the x and y components?

• Because the values are rounded

• Because the values are positive

• Because the values are negative

• Because the values are exact

How do the calculated components verify the vector's position in the third quadrant?

• Both components are positive

• Both components are zero

• Both components are negative

• One component is positive, and one is negative