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,
\(cos\theta=\frac{V_{y}}{V}\)
\(V_{y} =Vcos\theta\)
In the triangle OAC, the angle AOC \(is\ 90-\theta\)
\(cos[90-\theta]=\frac{V_{x} }{V}\)
\(sin\theta=\frac{V_{x} }{V}\) ∵ 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]
