What is the Correct Theta Angle for Vector Degrees Problem?

In summary, the homework equation A=-4.00+8.00 is not resolving to a specific angle because theta is in the third quadrant. To find the angle in the correct quadrant, you must add 180 degrees.
  • #1
Bottomsouth
27
0

Homework Statement



Ax= -4.00 , Ay= -8.00
Please give your answer in the interval (0,360) degrees for theta.




Homework Equations



Theta = ______ degrees

The Attempt at a Solution



I tried inverse of tangent (-8/-4) = 63.4 degrees for theta, but its telling me I am wrong. Tried the degree in negative and the computer showed up wrong also. Any Ideas?
 
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  • #2
Bottomsouth said:
Ax= -4.00 , Ay= -8.00


I tried inverse of tangent (-8/-4) = 63.4 degrees for theta, but its telling me I am wrong. Tried the degree in negative and the computer showed up wrong also. Any Ideas?

Hmmm... well just looking at Ax and Ay, what quadrant does A lie in? Does theta=63.4 degrees lie in that quadrant? :wink:

The problem is that the inverse tangent of (Ay/Ax) always returns a value between 0 and 180 degrees. But the tangent function has a period of 180 degrees, so tan(theta)=tan(theta+n*180)=Ay/Ax implies that theta=ArcTan(Ay/Ax)-n*180 for some integer value of n and not just theta=ArcTan(Ay/Ax).
 
  • #3
Remember the unit circle. The angle is in the third quadrant.
 
  • #4
It is in the 3rd quadrant making it positive for tangent. Just what would the variable n be?

Thanks for the help, appreciate it
 
  • #5
Got it now, since its int he 3rd quadrant we add 180 degrees. I knew it was something so simple. so its 243.4 degrees for theta.

Thanks,
 
  • #6
Choose n such that your angle is in the correct quadrant. In this case, what are the limits of n?
 
  • #7
Bottomsouth said:
It is in the 3rd quadrant making it positive for tangent.

Exactly; A is in the 3rd quadrant.

The tangent is positive in both the third quadrant and the first quadrant, and the arctangent always returns a value in the first to quadrants. That is why you are getting an angle that is in the first quadrant.

Just what would the variable n be?

Since A is in the 3rd quadrant, 'n' will be any integer that gives a theta in between 180 degrees and 270 degrees. In this case, n=-1 should do nicely.
 
  • #8
Bottomsouth said:
Got it now, since its int he 3rd quadrant we add 180 degrees. I knew it was something so simple. so its 243.4 degrees for theta.

Thanks,

Welcome :smile:
 

FAQ: What is the Correct Theta Angle for Vector Degrees Problem?

What is the Vector Degrees Problem?

The Vector Degrees Problem is a mathematical problem that involves finding the direction and magnitude of a vector in a given coordinate system. It is commonly encountered in physics, engineering, and other fields that deal with vector quantities.

How is the magnitude of a vector calculated?

The magnitude of a vector is calculated by taking the square root of the sum of the squared components of the vector. In other words, if a vector has components x and y, its magnitude can be calculated as √(x² + y²).

What does the direction of a vector represent?

The direction of a vector represents the angle at which the vector is pointing in relation to a given coordinate system. This angle can be measured in degrees or radians.

What is the difference between a vector and a scalar?

A vector is a quantity that has both magnitude and direction, while a scalar is a quantity that only has magnitude. For example, velocity is a vector quantity because it has both speed (magnitude) and direction, while temperature is a scalar quantity because it only has magnitude.

How is the Vector Degrees Problem used in real-world applications?

The Vector Degrees Problem is used in a variety of real-world applications, such as calculating the trajectory of a projectile in physics or determining the direction and speed of wind currents in meteorology. It is also used in navigation systems, computer graphics, and other areas that involve the use of vectors.

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