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August 4th, 2019, 02:53 AM  #1 
Newbie Joined: Aug 2019 From: Hong Kong Posts: 4 Thanks: 0  Domain Of Validity For Trigonometric Identities
Does anyone know how to find the domain of validity for trigonometric identities? There doesnt seem to be much tutorials on this topic on youtube/online. Can anyone explain to me step by step since I have absolutely no clue how to find it? 
August 4th, 2019, 03:39 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond 
Can you figure out where $\cos\theta$, $\sin\theta$ are equal to 0?

August 4th, 2019, 03:43 AM  #3  
Newbie Joined: Aug 2019 From: Hong Kong Posts: 4 Thanks: 0  Quote:
cos(x) = 0 in pi/2, 3pi/2, 5pi/2, so the multiples of pi/2? sin(x) = 0 in pi, 2pi/ 3pi, so the multiples of pi ? is this right ? so csc(x) = 1/sin(x), meaning the domain of validity is all real numbers except for the multiples of pi? The correct answer is all real numbers except for pi/2 though, why is that so? Last edited by Tsepten; August 4th, 2019 at 03:47 AM.  
August 4th, 2019, 06:05 AM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587  Quote:
 
August 4th, 2019, 06:21 AM  #5 
Newbie Joined: Aug 2019 From: Hong Kong Posts: 4 Thanks: 0  Oh I meant, what I got was 'domain of validity is all real numbers except for multiples of pi' (which is B), but D is the correct answer. If csc(x) = 1/sin(x), and sin(x) = 0 in multiples of pi, shouldn't the answer be: domain of validity is all real numbers except for multiples of pi? Last edited by skipjack; August 4th, 2019 at 11:03 AM. 
August 4th, 2019, 07:21 AM  #6  
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587  Quote:
$\sin{x} \ne 0 \implies x \text{ cannot be a whole multiple of }\pi = \text{ even multiples of }\frac{\pi}{2}$ therefore, $x \text{ cannot be any multiple of }\frac{\pi}{2}$, which matches up with choice D. Last edited by skipjack; August 4th, 2019 at 11:04 AM.  
August 4th, 2019, 04:34 PM  #7  
Newbie Joined: Aug 2019 From: Hong Kong Posts: 4 Thanks: 0  Quote:
Last edited by skipjack; August 4th, 2019 at 07:20 PM.  
August 4th, 2019, 06:01 PM  #8 
Math Team Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1587  Yes.
Last edited by skipjack; August 4th, 2019 at 07:20 PM. 

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domain, identities, trigonometric, validity 
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