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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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bob bundy
2013-06-08 04:11:13

............. 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

debjit625
2013-06-08 03:32:38

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...

bob bundy
2013-06-08 03:28:48

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

anonimnystefy
2013-06-08 02:22:37

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.

bob bundy
2013-06-08 01:59:32

Tell me more please.

Bob

anonimnystefy
2013-06-08 01:49:59

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

bob bundy
2013-06-08 01:46:26

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

debjit625
2013-06-08 00:57:36

And thanks Bob and anonimnystefy for the reply

debjit625
2013-06-08 00:55:33

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

anonimnystefy
2013-06-07 23:09:48

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

bob bundy
2013-06-07 20:22:39

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.

debjit625
2013-06-07 18:22:48

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

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