# When and how do I use sin and cos regarding 2-D collisions?

• JohnMC
In summary, the conversation discusses the use of sin and cos in the components of two-dimensional collisions. The person is trying to understand why sin is used for the East component and cos for the North component in one question, but in a different question, the sin and cos are switched. They realize that it has to do with how the angle is measured in relation to the sides of a triangle. The expert provides a diagram and explains that sin is used for the opposite side and cos for the adjacent side, depending on the angle. Eventually, the person understands and thanks the expert for their help.
JohnMC
I think what I'm doing is overkill because all I want to know is when to use sin and cos in the components regarding (isolated) two-dimensional collisions. I'm just showing more content because it might help for context. Also, there are more steps in order to find the final velocity which is why you can see some steps cut off, but I didn't bother posting more pictures of it because I thought it was irrelevant from then on as I am only looking for why sin and cos are used.

## Homework Statement

On QUESTION #1 III., why is sin used in the East component and cos used in the North component, when in QUESTION #2 II., a different but ultimately similar question, the sin and cos are switched? Please feel free to click through the images in order for context. Also, how do I know if I should label the components East and North? Why not other compass directions? I hope I'm making some sense :P

QUESTION #1
I. http://bayimg.com/image/oajpoaaca.jpg
II. http://bayimg.com/image/aajajaacb.jpg
IV. http://bayimg.com/image/cajaaaacb.jpg
V. http://bayimg.com/image/cajaoaacb.jpg

QUESTION #2
I. http://bayimg.com/image/cajcpaacb.jpg
II. http://bayimg.com/image/dajcmaacb.jpg
III. http://bayimg.com/image/eajcjaacb.jpg

N/A

## The Attempt at a Solution

Looked at sine laws, properties of triangles, and so far I have found nothing I can apply it to. Please forgive me if I'm asking such a simple question.

Last edited by a moderator:
it is because of how the angle is measured.

sin =opp/hyp

in 3, the east is opposite to the angle, so the east component is hyp*sin, similarly the north is adjacent to the angle. Understand?

I would like to say that I understand what you mean, but sadly I don't. Although I think I found out a way how and when to use sin and cos. Wordings such as [12.0 E of N] use East for sin and North for cos; while [12.0 N or E] use East for cos and North for sin. Was this what you meant by "because of the how angle is measured"? My apologies for failing to understand

JohnMC said:
I would like to say that I understand what you mean, but sadly I don't. Although I think I found out a way how and when to use sin and cos. Wordings such as [12.0 E of N] use East for sin and North for cos; while [12.0 N or E] use East for cos and North for sin. Was this what you meant by "because of the how angle is measured"? My apologies for failing to understand

See this diagram:

http://img16.imageshack.us/img16/3596/diagrm.jpg

Lets call DAC=α (alpha) and CAB=β

$$cos \alpha =\frac{adjacent}{hypotenuse}= \frac{AD}{AC}$$

$$sin\alpha = \frac{opposite}{hypotenuse}= \frac{DC}{AC}$$

Consider triangle ABC,

$$sin \beta = \frac{opposite}{hypotenuse}=\frac{BC}{AC}$$

$$cos \beta=\frac{adjacent}{hypotenuse}= \frac{AB}{AC}$$

Do you understand what I meant by how the angle is measured now?

Last edited by a moderator:
Thanks so much! I already knew the properties of sin and cos as shown in your second post, but it was just the thought of using East and North as a property of a triangle in 2-D collisions and matching it with sin and cos that confused me. I read your first post again and I finally figured it out. Again, thank you :)

## 1. What is the difference between sin and cos in 2-D collisions?

Sin and cos are both trigonometric functions used to calculate the relationship between sides and angles in a right triangle. In the context of 2-D collisions, sin is used to calculate the vertical component of velocity, while cos is used to calculate the horizontal component of velocity. This is because the vertical and horizontal directions are perpendicular to each other, just like the sides of a right triangle.

## 2. When should I use sin and cos in 2-D collisions?

You should use sin and cos whenever you need to calculate the components of velocity or acceleration in the vertical and horizontal directions. This is important in 2-D collisions because objects can move in multiple directions at once, and it is necessary to break down their motion into these separate components.

## 3. How do I determine the angle in a 2-D collision?

The angle in a 2-D collision can be determined by using the inverse trigonometric functions, such as arcsin or arccos. These functions allow you to find an angle given the ratio of sides in a right triangle. Once you have the angle, you can use sin and cos to calculate the vertical and horizontal components of velocity.

## 4. Do I always need to use sin and cos in 2-D collisions?

No, you do not always need to use sin and cos in 2-D collisions. These functions are only necessary when the motion of an object is not purely vertical or horizontal. If an object is moving in a straight line, you can simply use the traditional equations of motion without needing to break down the velocity into its components.

## 5. Can I use sin and cos to calculate the final velocity in a 2-D collision?

Yes, you can use sin and cos to calculate the final velocity in a 2-D collision. By using trigonometric functions, you can determine the components of velocity for each object involved in the collision and then combine them to find the final velocity. This is important in analyzing the outcome of a collision and understanding the conservation of momentum and energy.

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