A vector A is shown below. The x and y components of the vector are, respectively,
A) A sin $\alpha$, A cos $\alpha$) or A sin $\theta$, A cos$\theta$).
B) A sin $\alpha$, A cos $\alpha$) or A cos $\theta$, A sin $\theta$).
C) A sin $\alpha$, A sin $\alpha$) or A sin $\theta$, A cos $\theta$).
D) A cos $\alpha$, A cos $\alpha$) or A sin$\theta$, A cos $\theta$).
E) A cos $\alpha$, A cos $\alpha$) or A cos $\theta$, A cos $\theta$).

Question

A vector A is shown below. The x and y components of the vector are, respectively, 
A) A sin $\alpha$, A cos $\alpha$) or A sin $\theta$, A cos$\theta$). 
B) A sin $\alpha$, A cos $\alpha$) or A cos $\theta$, A sin $\theta$). 
C) A sin $\alpha$, A sin $\alpha$) or A sin $\theta$, A cos $\theta$). 
D) A cos $\alpha$, A cos $\alpha$) or A sin$\theta$, A cos $\theta$). 
E) A cos $\alpha$, A cos $\alpha$) or A cos $\theta$, A cos $\theta$).

Quizplus · Accepted Answer

To find the components of the vector, we can use trigonometry. Let the angle between the vector and the x-axis be θ.

The x-component of the vector is given by A cos(θ), which is equivalent to A cos(α).

The y-component of the vector is given by A sin(θ), which is equivalent to A sin(α).

Therefore, the best choice is B, where the x-component of the vector is given by A cos(α) or A cos(θ) and the y-component of the vector is given by A sin(α) or A sin(θ).

A Vector a Is Shown Below α\alphaα , a Cos α\alphaα ) or a Sin

A Vector a Is Shown Below $\alpha$ , a Cos $\alpha$ ) or a Sin