Assigning cosine and sines for axes

[physlexic]

Homework Statement

Hey everyone, I'm horrible at physics so bear with me if it's a really easy question.
I was working a problem out, where I assigned my x-axis with cosine, and my y-axis with sine, like how I always thought it should be.

However, in the solution, they assigned sine for the x-axis and cosine for the y-axis and therefore my results were backwards for T1 and T2. Was this a mistake in the book or in my understanding? If it's me, can someone please explain why the x-axis is given sine and the y-axis is given cosine?

Thanks. I also provided a picture of the problem.

Homework Equations

The Attempt at a Solution

Like I said I attempted the problem and I got the correct answers except my T1 and my T2 are mixed up because I put my x-axis as cos and my y-axis as sine, while the book did opposite. [/B]

 

[SteamKing]

Your problem lies in a faulty understanding of basic trigonometry. You don't assign the sine and cosine to this axis or that axis, a priori. What you do is analyze the given problem and apply trigonometry to solve for the components, the unknowns, whatever.

In the problem above, you should draw the triangles formed by T₁ and T₂ with the coordinate axes and compute the components of each vector.
Study Fig. 4.28 in particular. Sometimes, the way a book shows how to calculate the components of a given vector may not be the only way. That's where drawing the triangles helps.

 

[physlexic]

I understand my math is rusty, I haven't been in a math course or any course that requires math in over three years, I just went back to school.
Can anyone please give me a thorough explanation? I've been googling but I can't seem to find any tutorials or articles to help me determine whether an axis will be calculated with cosine or sine so I will know with confidence every time :/
Every single problem I've done and encountered so far in this physics course has always been cosine in the x-axis and sine in the y-axis and now this is so confusing to see that they can actually change depending on the problem and I just cannot see it.
When I draw the triangles then what? How do I determine by drawing the triangles?

 

[SteamKing]

If you haven't been in a math course in three years, then you definitely should do some refresher work on your trigonometry, especially on how the sine and cosine of an angle are determined.

Just because all of the problems you have worked thus far showed the cosine on the x-axis, it does not necessarily follow that the cosine must lie on the x-axis all the time.

To get down to specific cases, in the problem illustrated in the OP, Fig. 4.28, the vector T₁ forms the hypotenuse of the triangle whose acute angle of 10° is measured from the y-axis. The vertical component of T₁ is thus T₁ * cos 10°. Likewise, the horizontal component is T₁ * sin 10°.

Check out the definition of sine and cosine in this article:

http://en.wikipedia.org/wiki/Trigonometry

Look at the 'Overview' Section.

 

[physlexic]

Okay I think I understand in my own terms, for example, the y-axis is on the adjacent side of where 10 degrees is therefore adjacent means cosine...and opposite to that degree is sine which lies horizontal, therefore the x-axis. Thanks for the explanation, it did take me quite a while to register it lol.