Polar Coordinates: Solving for Angle in Second Quadrant | 59.1 Degrees

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SUMMARY

The discussion centers on calculating the angle of a vector in the second quadrant, specifically addressing an angle of 59.1 degrees from the positive x-axis. The correct calculation for the angle from the positive x-axis is 180 degrees minus 59.1 degrees, resulting in an angle of 120.9 degrees. The magnitude of the vector, derived from its components of -24.5 units (x) and 41.0 units (y), is confirmed to be 47.8 units using the Pythagorean theorem. The sine function is then applied to find the angle, affirming the need to adjust for the quadrant.

PREREQUISITES
  • Understanding of polar coordinates and quadrants
  • Proficiency in trigonometric functions, specifically sine
  • Familiarity with the Pythagorean theorem for magnitude calculation
  • Knowledge of vector components and their representation
NEXT STEPS
  • Study the properties of angles in different quadrants
  • Learn about vector addition and subtraction in two dimensions
  • Explore trigonometric identities and their applications in vector analysis
  • Practice solving problems involving polar coordinates and Cartesian coordinates
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Students studying physics or mathematics, particularly those focusing on vector analysis and polar coordinates, as well as educators seeking to clarify concepts related to angles in different quadrants.

chocolatelover
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Homework Statement



The angle is 59.1, which is in the second quadrant. Give the angle from the positive x-axis.

Homework Equations





The Attempt at a Solution



180-59.1=120.9

Does that look right?

Thank you very much
 
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chocolatelover said:
The angle is 59.1, which is in the second quadrant. Give the angle from the positive x-axis.
Quadrant one is from 0 to 90 degrees. Quadrant two is 90 to 180.
 
Thank you very much

Do you see where I went wrong?

A vector has an x component of -24.5 unites and a y component of 41.0 units. Find the magnitude and direction of this vector (from the positive x-axis)

I got 47.8 by doing (41.0)^2 + (-24.5)^2=c^2
c=47.8 units

In order to find the magnitude I did sin(theta)=41.0/47.8
=59.1 I need the magnitude from the positive x-axis. Would I then take 180-59.1?

Thank you
 

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