Find the x and y components of the following displacement.

[1irishman]

Homework Statement

20m 52deg W of N

Homework Equations

trig functions

The Attempt at a Solution

I got 20cos52=12.3m west
and 20sin52=15.8m north

yet the answer in the book says 12.3m north and 15.8m west. I don't understand...I thought cos was the x component and sin was the y component. so 15.8 m north is y and 12.3m west is x no? Please help me understand how the triangle and its components would look so i may recreate on paper?
Thank you.

 

[Proximity]

The angle is 52 degrees west of north. So you start at north and rotate 52 degrees to the left. The triangle will look similar to this:

Angle B -> |\
           | \
           |__\ <- Angle A

Angle A is 38* and Angle B is 52*.

Hope this helps.

 

[1irishman]

I thought angle A would be 52*

 

[Proximity]

Take a look at this:

The angle 52* West of North results in line c (note that in my pretty drawing, angle C and side c have no relation). Angle C is 52*, and since the axis are perpindicular, angle A + angle C needs to equal 90*, so A is equal to 38*.

So then cos(A) = b / c -> b = c * cos(A)
and, sin(A) = a / c -> a = c * cos(A)

 

[1irishman]

I figured it out a different way, but thank you for the help anyway.
I got Ry/20=cos52* so Ry=20cos52*=12.3m north
I got Rx/20=sin52* so Rx=20sin52* =15.8m west

 

[1irishman]

how do i get graphics like that to draw triangles etc?

 

[Proximity]

I just used paint.