Find Beta of <60,-50,40>: Solving the Equation

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In summary, the angle β of a vector with components <60, -50, 40> can be found using the equation Cosine β = Ay/lAl and rounding the answer to two significant figures. The correct response for this angle is 125 degrees.
  • #1
xtrubambinoxpr
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Homework Statement



Find Beta of <60,-50,40>

Homework Equations



Cosine β = Ay/lAl


The Attempt at a Solution



lAl = 87.74964387

So its arccos(-50/87.75) = 124.62

express to 2 significant figures and it keeps telling me I am wrong. I rounded to 125. kept at 124.62.. etc.
 

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  • #2
And i got the answer book telling me this
 

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  • #3
The book answers are clearly expressed to three significant figures. What is your correct response for the angle you determined expressed to two significant figures?
 
  • #4
Online it tells me to do 2 sig figs.
 
  • #5
PhanthomJay said:
The book answers are clearly expressed to three significant figures. What is your correct response for the angle you determined expressed to two significant figures?
And it's 125 degrees
 
  • #6
xtrubambinoxpr said:
And it's 125 degrees
No, that is three significant figures. What is 124.62 degrees expressed to two significant figures??
 
  • #7
PhanthomJay said:
No, that is three significant figures. What is 124.62 degrees expressed to two significant figures??
I honestly don't know because it clearly has 3 at 125
How would I make that 2 sig figs
 
  • #8
xtrubambinoxpr said:
I honestly don't know because it clearly has 3 at 125
How would I make that 2 sig figs
I am not an expert on significant figure rules, but you can find them through Google and other search engines. But here is a hint: 141.635 rounded to four sig figs is 141.6. If rounded to three sig figs it is 142; that same number rounded to two sig figs is 140. And that same number rounded to one sig fig is 100.
 

1. What is the equation for finding the beta of a vector?

The equation for finding the beta of a vector is:
β = arctan (y / √(x^2 + z^2))
Where x, y, and z are the components of the vector.

2. How do you solve for the beta of a given vector?

To solve for the beta of a given vector, plug in the values of the vector's components into the equation:
β = arctan (y / √(x^2 + z^2))
Make sure to use the correct units and follow the order of operations to find the value of beta.

3. What does the beta value represent in a vector?

The beta value represents the angle between the vector and the y-axis in a three-dimensional coordinate system. It is measured in radians and ranges from -π/2 to π/2.

4. Can the beta value be negative?

Yes, the beta value can be negative. It depends on the direction of the vector and its relationship to the y-axis. A positive beta value means the vector is above the y-axis, while a negative beta value means the vector is below the y-axis.

5. How does finding the beta of a vector relate to other mathematical concepts?

Finding the beta of a vector is related to trigonometry, as the equation involves the use of arctangent. It is also related to linear algebra, as it is used to calculate the angle between two vectors in a three-dimensional space. Additionally, it is an important concept in physics, particularly in determining the direction of forces acting on an object.

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