Cosine, Sin, Tangent when find force/tension

[lokobreed]

Ok... so I had this down and now I am all confused ;/

I am not posting in the homework sections because its not for homework although I will gie an example of a problem... I just want to understand why/how they use these to find the force/tension...

Example:
A 20 kg loudspeaker is suspended 2m below the celing by two cables that are each 30* from vertical. What is the tension in the cables?
For this I will cable 1 T1 and cable 2 T2.

So to find the X compenent of forces
since the x would use the 30 degree angle and it would be using the hyp and adjacent sides I will use the cos of the angle to find them
-T1x + T2x = 0 N --> -T1 COS 30 + T2 Cos 30 = 0

Now where I am confused is how to find the Y compent and why you would do it the way you do... I know you use sin but I just don't understand how you can use the opposite angle if it is not known... perhaps I am missing something ... please help!

 

[S_Happens]

You don't use a different angle. You use sine of the same angle, which instead of adjacent over hypotenuse as it was for cosine, is opposite over hypotenuse.

There is no "x uses the 30 degree angle" and y uses the opposite angle. Sine and Cosine can relate the angle and two sides of a triangle. With three variables, you need to know two to solve for the third.

Also, in this case if one angle given is 30, then you do indeed know all the other angles of the triangle. This is all done by right triangles, which means one angle has to be 90.

 

[lokobreed]

Thank you! What you said just made me remember everything somehow!
Thank you!

 

[S_Happens]

Everybody gets one.

J/k. Glad I could help.

 

[PJC01]

I can provide some insight into how trigonometry can be used to find force or tension in a given situation. In this example, the use of cosine, sine, and tangent can help determine the tension in the cables supporting the loudspeaker.

Firstly, it is important to understand that the tension in the cables is a vector quantity, meaning it has both magnitude and direction. In this case, the direction is determined by the angle of the cables from vertical. The magnitude of the tension is what we are trying to find.

To find the tension, we need to break it down into its horizontal and vertical components. This is where cosine and sine come into play. Cosine is used to find the horizontal component of tension, while sine is used to find the vertical component. In this example, the horizontal component is represented by T1x and T2x, while the vertical component is represented by T1y and T2y.

Using the given angle of 30 degrees and the weight of the loudspeaker, we can create a diagram and apply trigonometric principles to find the tension. The cosine of an angle is equal to the adjacent side divided by the hypotenuse, while the sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the hypotenuse is the tension in the cables, and the adjacent and opposite sides are the horizontal and vertical components, respectively.

To find the tension, we can set up equations using the horizontal and vertical components. In this example, the horizontal components are equal to each other and the vertical components are equal to the weight of the loudspeaker. Solving these equations will give us the magnitude of the tension in the cables.

In summary, trigonometric functions such as cosine, sine, and tangent can be used to find force or tension in a given situation by breaking it down into its horizontal and vertical components. These functions allow us to relate the angle of the cables to the magnitude of the tension in a mathematical way. I hope this explanation helps clear up any confusion you may have had.