Question

Suppose a vector V makes an angle (theta) with respect to the y axis. What could be the x and y component of the vector V? Express your answers in terms of the variables V and (theta) separated by a comma.

Answer 1

As pet the question the vector V makes an angle
`\theta` with respect to Y axis.

We are asked to calculate the the horizontal and vertical components i.e x component and y component.

Let us consider a two dimensional coordinate system which contains two axes X axis and Y axis which are perpendicular to each other.The vector V makes an angle
`\theta` with Y axis. Let the x component and y component is denoted as
`V_(x) \ and\ V_(y)` respectively.

The diagram is given below

In triangle OAB,

`cos\theta=(V_(y))/(V)`

`V_(y) =Vcos\theta`

In the triangle OAC, the angle AOC
`is\ 90-\theta`

`cos[90-\theta]=(V_(x) )/(V)`

`sin\theta=(V_(x) )/(V)` ∵ cos[90-Ф]=sinФ

`V_(x) =Vsin\theta`

Hence the x component and y component of the vector V is -

`Vsin\theta\ and\ Vcos\theta` [ans]