My Math Forum Negative Theta Angle

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 May 11th, 2018, 08:23 PM #1 Member   Joined: Aug 2017 From: India Posts: 54 Thanks: 2 Negative Theta Angle If you take a circle, the angle theta varies from 0 to 360 Degrees. What exactly is negative angle like -30 etc? I mean to say 330 is also -30 degrees? I am confused? Last edited by skipjack; May 12th, 2018 at 05:34 AM.
 May 11th, 2018, 08:57 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,949 Thanks: 1141 Math Focus: Elementary mathematics and beyond The sign of an angle is generally taken to be the direction from 0$^\circ$ with a negative value indicating clockwise motion.
 May 11th, 2018, 09:16 PM #3 Member   Joined: Aug 2017 From: India Posts: 54 Thanks: 2 So if I correctly understand, 0 to 360 degrees is counter clockwise direction and 0 to -360 (-20 etc.) is clockwise direction. Am I correct? Last edited by skipjack; May 12th, 2018 at 05:19 AM.
May 11th, 2018, 09:24 PM   #4
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Quote:
 Originally Posted by MathsLearner123 So if I correctly understand, 0 to 360 degrees is counter clockwise direction and 0 to -360 (-20 etc.) is clockwise direction. Am I correct?
Yes.

Last edited by skipjack; May 12th, 2018 at 05:19 AM.

May 11th, 2018, 09:29 PM   #5
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Quote:
 Originally Posted by MathsLearner123 So if I correctly understand, 0 to 360 degrees is counter clockwise direction and 0 to -360 (-20 etc.) is clockwise direction. Am I correct?
Yes. So $\cos270^\circ=\cos-90^\circ$ or, more generally, $\cos\alpha=\cos(\alpha+360k),k\in\mathbb{Z}$.

Last edited by skipjack; May 12th, 2018 at 05:19 AM.

May 12th, 2018, 05:34 AM   #6
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Quote:
 Originally Posted by MathsLearner123 If you take a circle, the angle theta varies from 0 to 360 Degrees.
That's a usable convention for polar coordinates, but other conventions are possible. A function of the angle needn't have 0 to 360 degrees as its domain, and needn't be periodic.

May 12th, 2018, 07:02 PM   #7
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 Originally Posted by skipjack That's a usable convention for polar coordinates, but other conventions are possible. A function of the angle needn't have 0 to 360 degrees as its domain, and needn't be periodic.
Is it possible for you to give examples or links corresponding to them? Thank you.

Last edited by greg1313; May 12th, 2018 at 07:20 PM.

 May 13th, 2018, 03:18 AM #8 Global Moderator   Joined: Dec 2006 Posts: 20,802 Thanks: 2149 You can find more detail and examples here.
 May 14th, 2018, 02:24 AM #9 Member   Joined: Aug 2017 From: India Posts: 54 Thanks: 2 My requirement is a kind of creation of sine wave using a look up table. So the 360 degrees is represented as 65536 an int value. The sampling frequency is the frequency of the pwm signal which 20KHz. I need to write a program for the same. I do not know what is the use of this sampling frequency. Why is it required? Please advise.

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