As pet the question the vector V makes an angle [tex]\theta[/tex] 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[tex]\theta[/tex] with Y axis. Let the x component and y component is denoted as [tex]V_{x} \ and\ V_{y}[/tex] respectively.
The diagram is given below
In triangle OAB,
[tex]cos\theta=\frac{V_{y}}{V}[/tex]
[tex]V_{y} =Vcos\theta[/tex]
In the triangle OAC, the angle AOC [tex]is\ 90-\theta[/tex]
[tex]cos[90-\theta]=\frac{V_{x} }{V}[/tex]
[tex]sin\theta=\frac{V_{x} }{V}[/tex] ∵ cos[90-Ф]=sinФ
[tex]V_{x} =Vsin\theta[/tex]
Hence the x component and y component of the vector V is -
[tex]Vsin\theta\ and\ Vcos\theta[/tex] [ans]
