Minutes, Degrees, Seconds to Radians

Click For Summary

Discussion Overview

The discussion revolves around converting an angle given in degrees, minutes, and seconds (12° 28' 4") into radians. Participants explore different methods for this conversion, including the application of known relationships between these units.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in applying the conversion factor of pi/180° to the problem.
  • Another participant suggests using the method previously discussed, emphasizing the conversion of seconds to degrees by noting that there are 3600 seconds in a degree.
  • A participant questions the initial difficulty, providing a step-by-step breakdown of the conversion process from seconds to minutes to degrees, ultimately leading to the multiplication by pi/180.
  • Some participants inquire about alternative methods for solving the problem, suggesting a focus on converting strictly to degrees before transitioning to radians.
  • A mathematical expression is presented that outlines the conversion from degrees, minutes, and seconds to radians, yielding a specific fraction involving pi.
  • One participant reflects on the process, indicating a sense of recollection regarding the conversion methods discussed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a single method for the conversion, as multiple approaches and questions about alternative solutions are raised throughout the discussion.

Contextual Notes

Some participants rely on specific relationships between units (e.g., seconds to degrees) without explicitly stating all assumptions, and there are unresolved steps in the conversion process that may depend on individual interpretations of the methods discussed.

mathdad
Messages
1,280
Reaction score
0
Express the following angle in radians.

12 degrees, 28 minutes, 4 seconds that is, 12° 28' 4".

I cannot apply pi/180° to this problem.
 
Mathematics news on Phys.org
Use the same method I posted in your other thread, and use the fact that there are 3600 seconds in a degree. :D
 
Why can't you "apply pi/180" here?

You know that there are 60 seconds in a degree don't you? So 4''= 4/60= 0.06667 minutes approximately and 28' 4'' is 28.06667 minutes. And you know, I hope, that there are 60 minutes in a degree so that 28.06667 minutes is 28.06667/60= 0.4678 degrees. 12 degrees, 28 minutes, 4 seconds is 12.4678 degrees. Multiply that by pi/180.
 
MarkFL said:
Use the same method I posted in your other thread, and use the fact that there are 3600 seconds in a degree. :D

Is there another way to solve this problem?
 
RTCNTC said:
Is there another way to solve this problem?

What you want to do is convert strictly to degrees, and then to radians.

$$12^{\circ}28'4''=\left(12+\frac{28}{60}+\frac{4}{3600}\right)^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{11221\pi}{162000}$$
 
It's all coming back to me now.
 

Similar threads

MHB How can you express an angle in radians without using pi/180°?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Can the same argument be used for both radians and degrees in the sine function?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Radians to Degrees, Minutes, Seconds
  • · Replies 4 ·
Replies
4
Views
3K
High School Udemy Quiz Question on Radians and Quadrants
  • · Replies 16 ·
Replies
16
Views
2K
MHB Angular Velocity - 2100 Revs in 3 Mins - 73.3 Rad/s
  • · Replies 4 ·
Replies
4
Views
4K
High School Venus and Jupiter Conjunction
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Why is it important to convert angle units when using trigonometric functions?
  • · Replies 8 ·
Replies
8
Views
2K
MHB Angular Speed of Smaller Wheel
  • · Replies 2 ·
Replies
2
Views
3K
MHB Angular and Linear Speed....Part 1
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad A Trick to Memorizing Trig Special Angle Values Table
  • · Replies 3 ·
Replies
3
Views
2K