Vector Decomposition and Trig in Tension Force Analysis

AI Thread Summary
In the discussion on vector decomposition and trigonometry in tension force analysis, participants clarify the roles of sine and cosine in relation to angles in right triangles. Sine is associated with the vertical component, while cosine corresponds to the horizontal component, based on trigonometric principles. The importance of understanding vector decomposition is emphasized, particularly in analyzing forces. Participants suggest drawing a labeled right triangle to visualize the tension force and its components. Overall, the conversation focuses on applying trigonometric functions to resolve forces in physics problems.
Scorry
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Homework Statement



This is a solved problem. It is attached. Why is sin theta horizontal, and cosine theta vertical?

Homework Equations



All relevant equations are given.

The Attempt at a Solution


The solution is given.
 

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Scorry said:

Homework Statement



This is a solved problem. It is attached. Why is sin theta horizontal, and cosine theta vertical?
You'll have to be more specific.
The short answer is: Because trigonometry says so.
 
Its been a while since I have seen trig. Can you explain how I should look at it? It says theta is relative to the vetical.
 
Are you familiar with SOH CAH TOA?
Can you draw a labelled right angled triangle with FT as the hypotenuse?
 
billy_joule said:
Are you familiar with SOH CAH TOA?
Can you draw a labelled right angled triangle with FT as the hypotenuse?
Yes remember those 3 trig functions. I can draw a right triangle with the hypotenuse labeled Tension force. Where are you going with this?
 
Scorry said:
Yes remember those 3 trig functions. I can draw a right triangle with the hypotenuse labeled Tension force. Where are you going with this?
I'm trying to ascertain what exactly you are having trouble with. Do you understand vector decomposition? Do you understand why you need to do it in this case? Can you use trig to find lengths of a right triangle sides?

'draw a labelled right angled triangle' = include all information you have. Orientation relative to x & y axis, theta, Label the other sides descriptively ie FT,X FT, Y. Using SOH CAH TOA, what are the lengths of the opposite and adjacent sides?
 

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