How to use arc tan to find an angle?

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SUMMARY

The discussion focuses on using the arctangent function to find the angle between two vector displacements in physics. Specifically, the angle can be calculated using the formula Arctan(Ry/Rx), where Ry and Rx represent the y and x components of the vector, respectively. The arctangent function provides the principal value of the angle between -90 and 90 degrees, which is essential for determining the angle relative to the positive x-axis. The example provided involves calculating the angle when R is 218.684158367 and the other displacement is 187.

PREREQUISITES
  • Understanding of vector components (Ry and Rx)
  • Familiarity with trigonometric functions, specifically arctangent
  • Basic knowledge of physics concepts related to displacement
  • Ability to perform calculations involving angles and vectors
NEXT STEPS
  • Learn how to calculate vector components from displacement values
  • Study the properties of the arctangent function and its periodicity
  • Explore applications of trigonometry in physics problems
  • Investigate how to handle multivalued outputs from trigonometric functions
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in vector analysis or trigonometric calculations in scientific contexts.

hasheesh786
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in physics we were doing a problem that essentially involved vectors and in the end we were left with 2 displacements. how would i find the angle between them if it was not a right triangle? i asked someone and they said that i could find it using artan(Ry/Rx) ...R being one of the displacements
 
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If Ry and Rx are the y and x components of a vector, then there is a right angle between them- the x and y axes are at right angles. So, yes, Arctan(Ry/Rx) is the angle the vector makes with the positive x axis. (Since tangent is periodic, arctan is multivalued. Arctan is the "principal" value between -90 and 90 degrees. Make sure that is what you want.)
 
HallsofIvy said:
If Ry and Rx are the y and x components of a vector, then there is a right angle between them- the x and y axes are at right angles. So, yes, Arctan(Ry/Rx) is the angle the vector makes with the positive x axis. (Since tangent is periodic, arctan is multivalued. Arctan is the "principal" value between -90 and 90 degrees. Make sure that is what you want.)

so if the R value is 218.684158367 and the other displacement is 187 how would i find the angle between them using the arc tan?
 

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