IGCSE/GCSE/O & A Level/IB/University Student Forum
Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: nid404 on September 08, 2009, 04:23:37 am
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Express 8 sin theta-15 cos theta in the form R sin(theta-alpha), where R > 0 and 0degress < alpha < 90degrees, giving the
exact value of R and the value of alpha correct to 2 decimal places.
Can somebody help me with this....plz guide me with the steps..astar plz help
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one more identity question...it's a little complicated for me to understand
Prove the identity
(cos x + 3 sinx)2 = 5 - 4cos2x + 3 sin2x.
Sir, can u list all the equations we need to know for AS trig...i mean equations relating the three functions (tan,sin and cos)
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one more identity question...it's a little complicated for me to understand
Prove the identity
(cos x + 3 sinx)2 ? 5 ? 4cos2x + 3 sin2x.
Sir, can u list all the equations we need to know for AS trig...i mean equations relating the three functions (tan,sin and cos)
wats the '?'.........
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one more identity question...it's a little complicated for me to understand
Prove the identity
(cos x + 3 sinx)2 ? 5 ? 4cos2x + 3 sin2x.
Sir, can u list all the equations we need to know for AS trig...i mean equations relating the three functions (tan,sin and cos)
wats the '?'.........
oopss....when i copy pasted it...the symbol changed...anyways i've corrected it
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ur question can u clear it nd post ...
i cant get the question properly ... the second tht is ...
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ur question can u clear it nd post ...
i cant get the question properly ... the second tht is ...
yup it's correct now
Can you answer it master786??
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one more identity question...it's a little complicated for me to understand
Prove the identity
(cos x + 3 sinx)2 = 5 - 4cos2x + 3 sin2x.
Sir, can u list all the equations we need to know for AS trig...i mean equations relating the three functions (tan,sin and cos)
is it 4cos2x and 3sin2x...or 2x
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i wil ltry :P
lost touch with identities .. is this C2 stuff ?
or higher ?
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i wil ltry :P
lost touch with identities .. is this C2 stuff ?
or higher ?
It's an AS question Pure maths
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oh great lets wait for astar :P
he wil answer it in no time :)
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one more identity question...it's a little complicated for me to understand
Prove the identity
(cos x + 3 sinx)2 = 5 - 4cos2x + 3 sin2x.
Sir, can u list all the equations we need to know for AS trig...i mean equations relating the three functions (tan,sin and cos)
is it 4cos2x and 3sin2x...or 2x
2x not superscript
haha master786 i knew astar could do it :P
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yea :P i hav done identities but inedexcel...C2 ..theC3 once might be the level of pure maths ... nd C3 i havent done yet :P
so yea astars the man now :P
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yea :P i hav done identities but inedexcel...C2 ..theC3 once might be the level of pure maths ... nd C3 i havent done yet :P
so yea astars the man now :P
no problem master...i can wait
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one more identity question...it's a little complicated for me to understand
Prove the identity
(cos x + 3 sinx)2 = 5 - 4cos2x + 3 sin2x.
Sir, can u list all the equations we need to know for AS trig...i mean equations relating the three functions (tan,sin and cos)
done
answer in the next post
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one more identity question...it's a little complicated for me to understand
Prove the identity
(cos x + 3 sinx)2 = 5 - 4cos2x + 3 sin2x.
Sir, can u list all the equations we need to know for AS trig...i mean equations relating the three functions (tan,sin and cos)
done
answer in the next post
Thanks adi...
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ko..soo the 3 identities v use are..
sin2x = 2sinx cos x
cos2x = cos2x - sin2x
sin2x + cos2x = 1
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k now first...simplify the LHS
therefore....RHs => cos2x + 6sinx cosx + 9sin2x
now the LHS => 5 - 4cos2x + 3sin2x
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lets break the LHS into 3 parts => 5 ; -4cos2x ; 3sin2x
now 5 = 5sin2x + 5cos2x
...-4cos2x = -4cos2x + 4sin2x
... 3sin2x = 6sinx cos x
(check the first 2 identities)
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so LHS => 5sin2x + 5cos2x -4cos2x + 4sin2x + 6sinx cos x
now cancel them and u get the RHS
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Express 8 sin theta-15 cos theta in the form R sin(theta-alpha), where R > 0 and 0degress < alpha < 90degrees, giving the
exact value of R and the value of alpha correct to 2 decimal places.
Can somebody help me with this....plz guide me with the steps..astar plz help
sry..cudnt solve this...
not done these types of sums in add. math
will still try though...
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ko..soo the 3 identities v use are..
sin2x = 2sinx cos x
cos2x = cos2x - sin2x
sin2x + cos2x = 1
---
k now first...simplify the LHS
therefore....RHs => cos2x + 6sinx cosx + 9sin2x
now the LHS => 5 - 4cos2x + 3sin2x
----
lets break the LHS into 3 parts => 5 ; -4cos2x ; 3sin2x
now 5 = 5sin2x + 5cos2x
...-4cos2x = -4cos2x + 4sin2x
... 3sin2x = 6sinx cos x
(check the first 2 identities)
----
so LHS => 5sin2x + 5cos2x -4cos2x + 4sin2x + 6sinx cos x
now cancel them and u get the RHS
hey thanx...i didn't think about splitting it and then using the identities
this will help me solve sums ahead
no probs if u can't solve it...we'll wait for astar :P
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Yes i will. I am also making some resource pages for my own website.
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ko..soo the 3 identities v use are..
sin2x = 2sinx cos x
cos2x = cos2x - sin2x
sin2x + cos2x = 1
---
k now first...simplify the LHS
therefore....RHs => cos2x + 6sinx cosx + 9sin2x
now the LHS => 5 - 4cos2x + 3sin2x
----
lets break the LHS into 3 parts => 5 ; -4cos2x ; 3sin2x
now 5 = 5sin2x + 5cos2x
...-4cos2x = -4cos2x + 4sin2x
... 3sin2x = 6sinx cos x
(check the first 2 identities)
----
so LHS => 5sin2x + 5cos2x -4cos2x + 4sin2x + 6sinx cos x
now cancel them and u get the RHS
hey thanx...i didn't think about splitting it and then using the identities
this will help me solve sums ahead
no probs if u can't solve it...we'll wait for astar :P
anytime..
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maybe astar is busy..
slvri can u try..?
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Express 8 sin theta-15 cos theta in the form R sin(theta-alpha), where R > 0 and 0degress < alpha < 90degrees, giving the
exact value of R and the value of alpha correct to 2 decimal places.
Can somebody help me with this....plz guide me with the steps..astar plz help
ok.......8 sin theta-15 cos theta has the form a sin theta + b cos theta where a=8 and b=-15.this can be expressed in the form in the form R sin(theta-alpha) where R = sqrt(a2+b2) and R cos alpha = a (or R sin alpha = b)
R = sqrt(82+(-15)2)=17
now R cos alpha = 8
17 cos alpha = 8
alpha = cos-1(8/17)=61.93 degrees
so 8sin theta-15cos theta = 17 sin (theta - 61.93)
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Express 8 sin theta-15 cos theta in the form R sin(theta-alpha), where R > 0 and 0degress < alpha < 90degrees, giving the
exact value of R and the value of alpha correct to 2 decimal places.
Can somebody help me with this....plz guide me with the steps..astar plz help
ok.......8 sin theta-15 cos theta has the form a sin theta + b cos theta where a=8 and b=-15.this can be expressed in the form in the form R sin(theta-alpha) where R = sqrt(a2+b2) and R cos alpha = a (or R sin alpha = b)
R = sqrt(82+(-15)2)=17
now R cos alpha = 8
17 cos alpha = 8
alpha = cos-1(8/17)=61.93 degrees
so 8sin theta-15cos theta = 17 sin (theta - 61.93)
Thanx a lot :))
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Express 8 sin theta-15 cos theta in the form R sin(theta-alpha), where R > 0 and 0degress < alpha < 90degrees, giving the
exact value of R and the value of alpha correct to 2 decimal places.
Can somebody help me with this....plz guide me with the steps..astar plz help
ok.......8 sin theta-15 cos theta has the form a sin theta + b cos theta where a=8 and b=-15.this can be expressed in the form in the form R sin(theta-alpha) where R = sqrt(a2+b2) and R cos alpha = a (or R sin alpha = b)
R = sqrt(82+(-15)2)=17
now R cos alpha = 8
17 cos alpha = 8
alpha = cos-1(8/17)=61.93 degrees
so 8sin theta-15cos theta = 17 sin (theta - 61.93)
Thanx a lot :))
no problem ;)
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Sorry I missed this. I am trying to do the templates for some maths notes I want to write for my own site.
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Sorry I missed this. I am trying to do the templates for some maths notes I want to write for my own site.
It's ok sir...you're so worked up..u need a break