Vector components on Tilted Axis

[LearninDaMath]

θ

Homework Statement

Find the components N$_{x}$ and N$_{y}$ of vector N in the tilted cooridinate system.

Homework Equations

cosθ = adg/hyp and sinθ= opp/hyp

The Attempt at a Solution

The correct answer is supposed to be
N$_{x}$ = -Nsinθ and N$_{y}$ = Ncosθ

The error is on the component vector N$_{x}$.

How do you find the component vectors and come up with a negative for N$_{x}$?

 

[Simon Bridge]

The x component of N is pointing in the -x direction.
That's what the minus sign is telling you.

You have to do this because the positive angle is measured from the y-axis and towards the negative x axis.
If you measured it towards the positive x-axis then the angle shown would be negative, and the sign would take care of itself.