Question

A vector with a magnitude of 46 is pointed at 320° from the positive x-axis. Break the vector into its x and y-components and provide the answer in component form.

Answer 1

To find the x and y-components of a vector with a magnitude of 46 at an angle of 320 degrees, use trigonometric functions after adjusting for the fourth quadrant, where cos is positive and sin is negative. The vector components are calculated as Vx = 46 × cos(320°) and Vy = 46 × sin(320°).

Step-by-step explanation:

To break a vector into its x and y-components, we use trigonometric functions cosine and sine. For a vector with a magnitude of 46 pointed at 320°, we calculate the x-component (Vx) by multiplying the magnitude with the cosine of the angle, and the y-component (Vy) by multiplying the magnitude with the sine of the angle. However, because the angle is given from the positive x-axis, and considering the standard position, the angle used in calculations should be transformed into standard polar coordinates where angles are measured counterclockwise from the positive x-axis.

The transformations for the angle would be:

• For 320°, which is in the fourth quadrant, we consider that cos(320°) is positive and sin(320°) is negative.

Using these principles:

Vx = 46 × cos(320°)
Vy = 46 × sin(320°)

Therefore, in component form, the vector (V) can be represented as:

V = (Vx, Vy)