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#1 2013-06-06 20:22:48

debjit625
Member
Registered: 2012-07-23
Posts: 89

Trigonometry Problem

Hi, guys

I tried but I can't  solve it...

If a,b are two different values of x lying between 0 and 2 pi (i.e.. 0 to 360 degrees) which satisfy the equation 6 cos x + 8 sin x = 9 ,find the value of sin(a + b).

Well what I did was I turned that equation into an quadratic equation and find the roots and also use the relation of the sum of the roots.But no luck my solution is getting no where....

here is what I got when I turned it into an quadratic...

Thanks


Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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#2 2013-06-06 22:22:39

bob bundy
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Registered: 2010-06-20
Posts: 6,121

Re: Trigonometry Problem

hi debjit625

I don't think that quadratic is correct.  If you square the equation you have

So where did the sinxcosx term go ?

You could try this:

and so get an expression for cos(x - y) where cos(y) = 6/10 .....

This enables you to work out values for a and b and hence sin(a+b).

I'm getting

I feel as though a solution should be possible without evaluating the angles and thus giving 'absolute' accuracy but I cannot find it yet.  Still thinking about this.  dizzy

Bob

ps.  Diagram was for a failed solution, but I cannot delete it at the moment.

View Image: debjit.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2013-06-07 01:09:48

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Trigonometry Problem

His quadratic is correct. Use cos(x)=sqrt(1-(sin(x))^2).


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#4 2013-06-07 02:55:33

debjit625
Member
Registered: 2012-07-23
Posts: 89

Re: Trigonometry Problem

Sorry for late reply...
Here is how I did






The answer in the book is sin(a + b) = 24/25 as bob got 0.96,@Bob but I didn't understood what you did... can you explain and why my equation is not working

Last edited by debjit625 (2013-06-07 03:48:18)


Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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#5 2013-06-07 02:57:36

debjit625
Member
Registered: 2012-07-23
Posts: 89

Re: Trigonometry Problem

And thanks Bob and anonimnystefy for the reply


Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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#6 2013-06-07 03:46:26

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,121

Re: Trigonometry Problem

hi debjit625

Apologies for thinking the quadratic was wrong.  But it gives

Which is not sin(a+b)

Still hoping for an analytic solution.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2013-06-07 03:49:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Trigonometry Problem

24/25 is the exact answer. We can use the roots of that quadratic.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#8 2013-06-07 03:59:32

bob bundy
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Registered: 2010-06-20
Posts: 6,121

Re: Trigonometry Problem

Tell me more please.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#9 2013-06-07 04:22:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: Trigonometry Problem

Hi Bob

The solutions are:

One is sin(a), the other is sin(b). Now calculate cos(a) and cos(b) from those and use the sine of angle sum formula.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#10 2013-06-07 05:28:48

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,121

Re: Trigonometry Problem

hi Stefy,

Thanks for the solution.  That's nice. I like questions to come out with exact answers ... takes me back to 1968 when we didn't have calculators or computers.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#11 2013-06-07 05:32:38

debjit625
Member
Registered: 2012-07-23
Posts: 89

Re: Trigonometry Problem

Yes dude it make sense now ,I tried to solve and after coming to this point I gave up

Thanks anonimnystefy and Bob for the help...


Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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#12 2013-06-07 06:11:13

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,121

Re: Trigonometry Problem

............. to this point I gave up

That looks ok to me.

9 into 2736 is304
4 into 304 is 76
4 into 76 is 19

So root 2736 is 3 x 2 x 2 root 19

It's beginning to look like Stefy's.  up

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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