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Old 18th September 2014, 02:53 AM   #1 (permalink)
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A maths: can some kind soul explain to me the solution of sin θ= 0?

Hi guys! I m a newbie here and I m currently slogging for my Os. There is a concept in trigo that is perplexing me.
The concept is as follows: why is the solution of sin θ = 0 0 and 180 but not 360 degrees? @_@
Many thanks to those who can explain to me.

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Old 18th September 2014, 08:21 AM   #2 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

You mean sin 0 = 0? 0 is the same as 360, in a practical environment it just means you've returned to the starting point. for example a pendulum, it's stable position where it will always be as time goes to infinity is vertically down. Taking that as the starting position, we can say that the final position no matter how we start to push or twirl the pendulum, is theta = 0, 360, 720... we don't care if it has twirled around 10 times, that is the input. we are usually always interested in the output or final result and the position is still vertically downwards, that's all that matters in a circle.

It's also useful to realise that sin theta is nothing more than describing the angle of a pendulum swinging around a pivot point. if you put a moving paper from right to left and traced the path of the pendulum or what the pendulum draws on the paper, you'll see a sine graph. Cos is when the paper is moving from top to bottom, that's why they are 90 degrees out of phase.

hope it helps

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Old 18th September 2014, 09:06 AM   #3 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

360 degrees is also a solution for sin theta = 0. This can be seen from the graph of y = sin x. The only reason why 360 degrees is not a solution could be the range of values of x, eg. if 0 <= x < 360. If the range includes 360 and the solution given does not include 360 degrees, throw away the book or worksheet cos it's wrong.

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Old 18th September 2014, 02:38 PM   #4 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Oh ok! I guess there is something wrong with the assessment book as the range stated is 0<_theta<_360.
I have got the concept after your through explaination, many thanks!

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Old 18th September 2014, 03:15 PM   #5 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Oh yeah. The ques goes like this 2 sinθ = 5 cos^2 θ - 5 (0<_θ<_360).
Ans: 0, 180, 203.6, 336.4

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Old 20th September 2014, 01:33 AM   #6 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Perhaps you misread the question as 0 ≤ θ ≤ 360 when it is actually 0 ≤ θ < 360?

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Old 20th September 2014, 06:16 PM   #7 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

I have the book before me. Only when hell freezes over would I have misread the question. Haha.

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Old 20th September 2014, 10:46 PM   #8 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Are you using some TYS? It is common for error to be printed in the answer booklet.

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Old 21st September 2014, 01:40 AM   #9 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Ah no, I m not doing tys; the book I am using is FBP complete guide for A maths.
Is there something odd with the ques and ans?

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Old 21st September 2014, 04:02 PM   #10 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

If the range is 0° ≤ θ ≤ 360°, then the answer should include 360°.
Your guide's answer is wrong.

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Old 21st September 2014, 07:23 PM   #11 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Yeah. This book, as I have found out, is choke full of errors.
It's definitely not my recommended book.

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Old 22nd September 2014, 11:12 PM   #12 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Originally Posted by Tyro View Post
Yeah. This book, as I have found out, is choke full of errors.
It's definitely not my recommended book.
It's great that you realise a particular book is bad and not blindly follow a bad book.

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Old 23rd September 2014, 08:12 PM   #13 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Yeah haha, gonna get some other books to practise as well as doing TYS.
A maths is a pretty tricky topic. I have to drill myself hard to ace it.

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Old 23rd September 2014, 09:13 PM   #14 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Originally Posted by Tyro View Post
Yeah haha, gonna get some other books to practise as well as doing TYS.
A maths is a pretty tricky topic. I have to drill myself hard to ace it.
ALL THE BEST!!!! If you have any questions, feel free to post here so we can help you!!! We have a lot of expert here. LOL!

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Old 23rd September 2014, 09:28 PM   #15 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Complicated ...

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Old 24th September 2014, 01:44 PM   #16 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Haha thanks. I will be so thankful for the help of the experts here.
All the best to those taking their exams too, let's use this forum to guide and aid one another so as to nail our exams!

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Old 24th September 2014, 01:53 PM   #17 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Complicated isn't it? There are loads of questions that r deliberately misleading — they seem tough at first but when you look at the answer, the solution is pretty clear but somehow you fail to nail down the concept behind the questions and so it would be very wasteful to throw away marks like this owning to lack of discernment.

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Old 2nd January 2015, 01:36 PM   #18 (permalink)
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Re: A maths: can some kind soul explain to me the solution of sin θ= 0?

Hi.

For trigonometry questions, it is very important to identify the range of the answer. For example, in the case where sin θ= 0, it can also be true for θ=1080, but it is typically not in the range. In most cases, if not all cases, a question without specifying a range of answer cannot have definite answers. This is very important in both Mathematics and Additional Mathematics.

I will be uploading assignments of Solving Trigonometric Equations on my website (http://horizonedu.wordpress.com) in the near future for students taking Additional Mathematics to try out.

Regards,
Jonathan Leong
Consultant (Education) of Division of Mathematics
Managing Director of Horizon Education Singapore

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