Question

In a coordinate system, a vector is oriented at angle  with respect to the x-axis. the y component of the vector equals the vector's magnitude multiplied by which trigonometric function?in a coordinate system, a vector is oriented at angle  with respect to the x-axis. the y component of the vector equals the vector's magnitude multiplied by which trigonometric function

Answer 1

The vector’s magnitude multiplied by the sine of the angle gives the y component.

Answer 2

We want to find the y-component of a vector given that we know the direction and magnitude of the vector, we will find:

y = Sin(θ)*V

If in a coordinate system we have a vector oriented at an angle θ with respect to the positive x-axis (where θ is measured counterclockwise) we can define the components of that vector as the catheti of a right triangle.

Similarly, the vector would be the hypotenuse of said triangle.

Then, the y-component would be the opposite cathetus for the given angle theta, so we can use the property:

Sin(θ) = (opposite cathetus)/(hypotenuse)

Sin(θ) = y/V

Where V is the magnitude of the vector, then we can write:

y = Sin(θ)*V

So we can see that the y-component is the magnitude of the vector times the sine function evaluated on the given angle.

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