Angle between the hands of a clock (IWTSE)

[TomK]

Homework Statement

Question: For a conventional clock, how many times does the minute hand make a right angle with the hour hand in one day (between midnight on two consecutive days)?

Relevant Equations

Circle formulae.

I understand this working all the way up until the '2n-1' part, where n is a positive integer.

I understand that delta theta is 90 degrees (i.e. pi/2 radians), as the hands are at right angles to each other.. I also understand where the angle equations are derived from and why you have to find the difference between them. I just don't know why '2n-1' was chosen as the multiplier for pi/2. Would someone be able to explain this?

 

[vela]

Try calculating $m\frac \pi 2$ for $m=0, 1, 2, \dots$. Which values of $m$ correspond to the angles you're looking for here?

 

[TomK]

Try calculating $m\frac \pi 2$ for $m=0, 1, 2, \dots$. Which values of $m$ correspond to the angles you're looking for here?

Thank you. I now understand that '2n-1' (or '2n+1') is meant to represent an odd integer, since if delta theta = 270 degrees the hands are still perpendicular. I got an answer of 44.5 (or 43.5, depending on the expression used) which rounds to 44, the correct answer.