# Find the x and y components of the following displacement.

• 1irishman
In summary, the angle is 52 degrees west of north, resulting in a triangle with angle A being 38 degrees and angle B being 52 degrees. Using trigonometric functions, we can calculate the components of the triangle, with the x component being 15.8m west and the y component being 12.3m north.
1irishman

20m 52deg W of N

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.

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:

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

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

Hope this helps.

I thought angle A would be 52*

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)

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

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

I just used paint.

## 1. What are x and y components in a displacement?

The x and y components in a displacement refer to the horizontal and vertical distances traveled, respectively. They represent the change in position in the x and y directions.

## 2. How do you find the x and y components of a displacement vector?

To find the x and y components of a displacement vector, you can use the Pythagorean theorem and trigonometric functions. The x component is given by the magnitude of the displacement multiplied by the cosine of the angle it makes with the x-axis. The y component is given by the magnitude of the displacement multiplied by the sine of the angle it makes with the y-axis.

## 3. What is the difference between a scalar and vector displacement?

A scalar displacement only has a magnitude, while a vector displacement has both magnitude and direction. Scalar displacements are described by a single value, while vector displacements are described by multiple components, such as x and y.

## 4. Can the x and y components of a displacement be negative?

Yes, the x and y components of a displacement can be negative. This indicates that the displacement is in the opposite direction of the positive axes. For example, a displacement with an x component of -5 and a y component of -3 would mean the object has moved 5 units to the left and 3 units downwards.

## 5. How are x and y components of a displacement related to each other?

The x and y components of a displacement are related through the Pythagorean theorem. The magnitude of the displacement is equal to the square root of the sum of the squares of the x and y components. This relationship allows us to find the total displacement, as well as the direction of the displacement using trigonometric functions.

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