Suppose a vector V⃗ makes an angle ϕ with respect to the y axis.What could be the x and y components of the vector V⃗ ?
Express your answers in terms of the variables V and ϕ separated by a comma.
Well, isn't V⃗ just a fancy way of saying "Vector V"? So we're talking about Vector V here. Now, if V⃗ makes an angle ϕ with respect to the y axis, we can break it down into its x and y components.
The x component would be V * cos(ϕ), because that's how you calculate the x component when you have an angle and the magnitude of the vector. And the y component would be V * sin(ϕ), because, you guessed it, that's how you calculate the y component.
So, to summarize, the x component of V⃗ is V * cos(ϕ), and the y component is V * sin(ϕ). There you have it, the components of V⃗ in terms of V and ϕ, separated by a comma.
To find the x and y components of a vector V⃗ making an angle ϕ with respect to the y-axis, we can use the trigonometric functions sine and cosine.
The x-component (Vx) of the vector V⃗ can be found using the formula:
Vx = V * cos(ϕ)
The y-component (Vy) of the vector V⃗ can be found using the formula:
Vy = V * sin(ϕ)
Therefore, the x and y components of the vector V⃗ would be V * cos(ϕ) and V * sin(ϕ), respectively.
Vx= Vsinϕ
Vy= Vcosϕ