IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: spiderman on September 15, 2009, 11:50:36 am

Title: tignometry query
Post by: spiderman on September 15, 2009, 11:50:36 am
Prove the following identity

(1-2sin^2@)/(cos@+sin@)==cos@-sin@


Pls help someone
Title: Re: tignometry query
Post by: Ghost Of Highbury on September 15, 2009, 12:15:42 pm
Quote from: spiderman on September 15, 2009, 11:50:36 am
Prove the following identity

(1-2sin^2@)/(cos@+sin@)==cos@=sin@


Pls help someone
wats the "=="

and how can cos @ = sin @
is the q correct?
Title: Re: tignometry query
Post by: spiderman on September 15, 2009, 12:19:10 pm
== means that we have to solve the left hand side to get an answer matching the rhs
Title: Re: tignometry query
Post by: astarmathsandphysics on September 15, 2009, 12:21:47 pm
think the rhs should be cos@-sin@
multuply both sides by cos@+sin@ to get
1-2sin2@=(cos@+sin@)(cos@-sin@)=cos2@-sin2@=cos2@

1-2sin2@=cos2@ is an identity
Title: Re: tignometry query
Post by: Ghost Of Highbury on September 15, 2009, 12:21:59 pm
Quote from: eddie_adi619 on September 15, 2009, 12:15:42 pm
wats the "=="

and how can cos @ = sin @
is the q correct?

ok..i assume this is the question

(1-2sin^2@)/(cos@+sin@)= cos@ - sin@

the answer-----------

1 - 2sin2@ = sin2@ + cos2@ - 2sin2@ = cos2@ - sin2@

cos2@ - sin2@ = (cos @ + sin @) (cos @ - sin @)

wen u divide it by (cos@+sin@)

it is = (cos @ + sin @) (cos @ - sin @) / (cos@+sin@) = (cos @ - sin @)

therefore LHS = RHS

is this the question?
Title: Re: tignometry query
Post by: spiderman on September 15, 2009, 12:28:30 pm
Tahnks ssooo much
Title: Re: tignometry query
Post by: spiderman on September 15, 2009, 12:39:55 pm
Please can someone help me with the 4th question in the attached past paper
Title: Re: tignometry query
Post by: astarmathsandphysics on September 15, 2009, 12:49:31 pm
i)The equilibrium is at y=3. c=3, the displacement of the curve from equilibrium. The amplitude a =6 and the perid from the gaph is pi so b=2pi/pi=2

ii)y=0 so 6sin(2x)+3=0 so sin(2x+3)=-0.5 so
2x=sin-1-0.5=-30

2x=180--30=210 x=105
2x=360+-30=330 so x=165
2x=540--30=570 so x=285
2x=720+-30=690 so x=345
Title: Re: tignometry query
Post by: spiderman on September 15, 2009, 12:52:39 pm
Thank you so much astar