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Which trigonometric function, when multiplied by a vector's magnitude, gives the y-component of a vector oriented at an angle with respect to the x-axis in a coordinate system?
- A Cos θ
- B Cot θ
- C Sin θ
- D Tan θ
That's Correct!
It's Wrong!
In a coordinate system, when a vector is oriented at an angle θ with respect to the x-axis, its y-component can be found using the sine function. The y-component (V_y) is equal to the vector's magnitude (V) multiplied by the sine of the angle (θ):
Vy=V sinθ
This relationship comes from the definition of the sine function in a right triangle, where the opposite side (y-component) is equal to the hypotenuse (vector's magnitude) multiplied by the sine of the angle. This is a fundamental concept in vector decomposition.
