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

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please explain

sorry i accidently posted twice

To determine the answer to this question, we will utilize the properties of right triangles in the coordinate system.

Let's consider a vector in a coordinate system that is oriented at an angle θ with respect to the x-axis. The vector will have two components: the x-component (horizontal) and the y-component (vertical).

To find the y component of the vector, we can use the magnitude of the vector multiplied by a trigonometric function.

In a right triangle, we have three sides: the hypotenuse, adjacent side, and opposite side.

In this case, the hypotenuse represents the magnitude of the vector, the adjacent side represents the x-component of the vector, and the opposite side represents the y-component of the vector.

Since we are interested in finding the y-component, we need to identify the trigonometric function that relates the opposite side (y-component) to the hypotenuse (magnitude).

The trigonometric function that relates these two sides is the sine function (sin θ). Therefore, the y-component of the vector equals the vector's magnitude multiplied by the sine of the angle θ.

In equation form, the y-component (y) can be expressed as:
y = magnitude * sin(θ)

So, the y-component of the vector is equal to the vector's magnitude multiplied by the sine of the angle θ.