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

To understand how to calculate the y component of a vector at a specific angle with respect to the x-axis, we can use trigonometric functions.

Let's assume that the magnitude of the vector is represented by the letter "r".

In a right triangle, the y component of the vector can be represented by the side opposite to the angle theta. To find this side, we can use the sine function.

The sine of an angle theta (sin(theta)) is defined as the ratio of the length of the side opposite to the angle (y component) to the length of the hypotenuse (magnitude of the vector).

So, sin(theta) = y component / r

By rearranging the equation and isolating the y component, we can calculate it:

y component = r * sin(theta)

Therefore, the y component of the vector is equal to the magnitude (r) multiplied by the sine of the angle (theta).

This is really basic. I know it is in your text, with a diagram. What does it say?