# Standard angles for vectors (Mechanics)

• Joe_mama69
Joe_mama69
Homework Statement
Just got done with my first week in phyiscs (mechanics) and I'm pretty confused on to find the standard angle, We are currently learning vectors, and for example we had a problem were we had to calculate R from A and B, A was like 30 degrees in the first qaudrant and B was 36 degrees in the 3rd qaudrant, and he wanted us to use the standard angles when we calcualted the compnents, and somehow he got 60 degrees as the standard angle for A and 216 for B. I understand that he added 180 to 36 to get 216 and subtracted 30 from 90 to get 60, but in another example, A was 35 degrees in the fourth quadrant, and B was 10 degrees in the third quadrant, in which he got 325 as the standard angle of A and 190 for B again I understand that he 10 to 180 to get 190 for B and subtracted 35 from 360 for A, but overall I am confused on when to subtract or add and from which number to add or subtract from. But like in "normal math" the calculations are different like 30 degrees int eh frist quadrant would just be 30 degrees and 35 degrees in the fourth quadrant would be 395 degrees, so whats going on.

Sorry i couldn't figure out how to upload an image here, so heres an imgur link with the two examples i described, they are exactly what my professor wrote on the board, he uses the term standard angle even though I don't think thats a common term used in physics or even math as i couldnt find anything on it.
https://imgur.com/a/7uScK3r
Relevant Equations
x component = magnitude * cos(standard angle)
y component = magnitude * sin(standard angle)
n/a

Joe_mama69 said:
Homework Statement: Just got done with my first week in phyiscs (mechanics) and I'm pretty confused on to find the standard angle, We are currently learning vectors, and for example we had a problem were we had to calculate R from A and B, A was like 30 degrees in the first qaudrant and B was 36 degrees in the 3rd qaudrant....
Hi @Joe_mama69 and welcome to PF.

Your figures are hard to understand without a diagram. For example when you say "B was 36 degrees in the 3rd qaudrant" it's ambiguous. 36º could relative to the -x axis or relative to the -y axis.

Imagine a pointer fixed at the origin and pointing to the right (along the +x axis). That's 0º. Standard angles are then measured anticlockwise (ACW) from this position.

For example:
- rotate the pointer 90º ACW and this direction is 90º (+y axis);
- rotate the pointer another 90º ACW and this direction is 180º (-x axis);
- rotate the pointer another 90º ACW and this direction is 270º (-y axis);
- rotate the pointer another 90º ACW and this direction is 0º (+x axis) (same thing as 360º);

For example, draw the following for yourself:

1.The pointer is in the 3rd quadrant with 36º beetween it and the -x axis, the standard angle is 180º + 36º = 216º.

2. The pointer is in the 3rd quadrant with 36º between it and the -y axis, the standard angle is 270º - 36º = 234º.

Joe_mama69 said:
Homework Statement: Just got done with my first week in phyiscs (mechanics) and I'm pretty confused on to find the standard angle, We are currently learning vectors, and for example we had a problem were we had to calculate R from A and B, A was like 30 degrees in the first qaudrant and B was 36 degrees in the 3rd qaudrant, and he wanted us to use the standard angles when we calcualted the compnents, and somehow he got 60 degrees as the standard angle for A and 216 for B. I understand that he added 180 to 36 to get 216 and subtracted 30 from 90 to get 60, but in another example, A was 35 degrees in the fourth quadrant, and B was 10 degrees in the third quadrant, in which he got 325 as the standard angle of A and 190 for B again I understand that he 10 to 180 to get 190 for B and subtracted 35 from 360 for A, but overall I am confused on when to subtract or add and from which number to add or subtract from. But like in "normal math" the calculations are different like 30 degrees int eh frist quadrant would just be 30 degrees and 35 degrees in the fourth quadrant would be 395 degrees, so whats going on.
Relevant Equations: x component = magnitude * cos(standard angle)
y component = magnitude * sin(standard angle)

n/a
Hello @Joe_mama69 ,

Well, I have never heard of something like 'the standard angle', so I wouldn't know how to find it, or what to do with it. Also, I have never seen any exercise where an angle was given as 'like 30 degrees in the first quadrant'. Is that really the verbatim text in the problem statement ? Or is it your way of describing something like a picture on the blackboard ?

##\ ##

The standard angle on a unit circle is defined as the angle starting at the positive x-axis and going counterclockwise the to the radius of interest. The arc-length between the positive x-axis and the radius of interest is a measure of the standard angle in radians.

Then it follows that
x component = magnitude * cos(standard angle)
y component = magnitude * sin(standard angle)

See how that matches the diagram you have.

Last edited:
Lnewqban
kuruman said:
The standard angle on a unit circle is defined as the angle starting at the positive x-axis and going counterclockwise the the radius of interest. The arc-length between the positive x-axis and the radius of interest is a measure of the standard angle in radians.

Then it follows that
x component = magnitude * cos(standard angle)
y component = magnitude * sin(standard angle)

See how that matches the diagram you have.
ahhh i think i get it now, i think i got confused becuase i thought the 30 degrees meant it would match the exact postion on the unit circle. Thank you so much!

## What are standard angles in vector mechanics?

Standard angles in vector mechanics refer to specific angles commonly used to describe the direction of vectors. These typically include 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, and 180° relative to a reference axis, usually the positive x-axis.

## Why are standard angles important in vector mechanics?

Standard angles are important because they simplify calculations and allow for easier communication of vector directions. They are often used in problems involving forces, motion, and field vectors, providing a common reference that can be universally understood.

## How do you calculate the components of a vector given a standard angle?

To calculate the components of a vector given a standard angle θ, you use trigonometric functions. If the vector has a magnitude $$V$$, the horizontal component $$V_x$$ is $$V \cos(θ)$$ and the vertical component $$V_y$$ is $$V \sin(θ)$$.

## What is the significance of the 90° and 180° angles in vector mechanics?

The 90° angle signifies that the vector is perpendicular to the reference axis, meaning it has no component along that axis. The 180° angle indicates that the vector is in the exact opposite direction of the reference axis, effectively reversing its direction.

## Can standard angles be used for 3D vectors?

Yes, standard angles can be extended to 3D vectors, but additional angles are needed to describe the direction fully. In 3D, vectors are often described using two angles: the azimuth angle (in the xy-plane) and the elevation angle (from the xy-plane up to the vector).

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