What formula is used to find the y-component of a vector?

What formula is used to find the y-component of a vector?

• A. y = r / sin(theta)
• B. y = r x tan(theta)
• C. y = r x cos(theta)
• D. y = r x sin(theta)

Answer: (D)

To find the y-component of a vector in a two-dimensional coordinate system, the correct formula involves the sine function. The y-component represents the vertical part of the vector and is calculated by multiplying the magnitude of the vector (r) by the sine of the angle (theta) that the vector makes with the horizontal axis. Thus, the formula y = r x sin(theta) appropriately captures this relationship, representing how much of the vector extends in the y-direction based on its angle from the x-axis. This concept is rooted in the basic definitions of trigonometric functions in the context of right triangles, where the sine function relates the opposite side (in this case, the y-component) to the hypotenuse (the magnitude of the vector). The use of sine here reflects the connection between the angle and the respective components in a vector’s representation.

To find the y-component of a vector in a two-dimensional coordinate system, the correct formula involves the sine function. The y-component represents the vertical part of the vector and is calculated by multiplying the magnitude of the vector (r) by the sine of the angle (theta) that the vector makes with the horizontal axis. Thus, the formula y = r x sin(theta) appropriately captures this relationship, representing how much of the vector extends in the y-direction based on its angle from the x-axis.

This concept is rooted in the basic definitions of trigonometric functions in the context of right triangles, where the sine function relates the opposite side (in this case, the y-component) to the hypotenuse (the magnitude of the vector). The use of sine here reflects the connection between the angle and the respective components in a vector’s representation.