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

The x component of the vector is given by A cosθ and the y component is given by A sinθ. In the given equation, θ is represented by α. So, the correct choices would be (A sinα, A cosα) or (A cosθ, A sinθ). The only option that matches this format is option B. Option A and D have mixed up the sin and cos terms, option C has sin terms for both components, and option E has only cos terms. Therefore, option B is the best choice.

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