Question

Problems on Tension.

When you have two vector components, how do you know when Tx or Ty is cos(theta) or sin(theta)?

I know that it depends on the triangle, but i can never seem to get it right.

Answer 1

first you should understand the basic idea behind dissecting a vector in to components and vectors itself. When you have to dissociate a vector in to components the resulting components should give the original vector in turn. for this purpose we use the triangular vector addition principle

Note: the way I have drawn those arrows, it's an essential thing to remember.
In most problems we dissect the vector in to perpendicular components (we can do it in many ways hence we can draw many triangles), because the magnitudes could be easily calculated using pythogoras theorem-only the magnitudes remember that pythogoras doesn't give the directions of the components. The triangular theorem is the tool that gives the directions. And actually we use triangular theorem for vector addition because it is true for all experimental purposes. And for the question, those Sine, Cos functions are derived from the basic trignometric definitions for a right angled triangle in order to calculate the magnitudes of the components.

\[T ^{2} =(TsinA)^{2}+(TcosA)^{2} ,,,>,,,,,, ; (\sin A)^{2} +(\cos A)^{2}=1\]

I hope this answer migt help you.... good luck

Answer 2

That was a good one, @indula. But, breaking it down further concerning your question @julesavv, there is a very simple way for you to understand the concept of the sin and cosine functions. Here:


Just to help you grab what indula was tryna explain. Best regards.