Math Is Fun Forum

careless25

Real Member

Registered: 2008-07-24

Posts: 560

Calculus I help!

Heres the question i cannot solve:

sin x + 8 cos x represented in the form Asin(x-y)

Thanks,

C25

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Calculus I help!

hi C25

The method for doing this is to 'force' it into the following format:

Asin(x-y) = Asinxcosy -Acosxsiny (use of compound angle formula; slight complication as you have a + sign between the elements))

so

sinx + 8cosx = 1sinx + 8cosx

= A(1/A  sinx  + 8/A cosx) where A =  sqr root (1 + 64) 

[This use of Pythagoras means there is a 'right angled triangle' with angle y where cosy = 1/A and siny = -8/A. Strictly no such triangle exists because of the minus 8; more usually there is no sign change when using the compound angle formula; but it won't matter as long as you get a 'y' that's over 180 degrees.] 

So, find A by the above Pythag. calculation and y by y = inv tan (8/1); this will be an acute angle; so now find the reflex angle that has cos positive and sin negative; so an angle between 270 and 360 is expected.

Hope that makes sense; I've got some jet lag today; post again if you need more clarification.

Bob

Last edited by Bob (2010-10-04 21:35:37)

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Children are not defined by school ...........The Fonz
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soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Calculus I help!

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careless25

Real Member

Registered: 2008-07-24

Posts: 560

Re: Calculus I help!

Thanks a lot both of you ...
Soroban thats a nice trick...took me a few minutes to understand but finally got it