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Offline spiderman

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AS Math queries
« on: September 03, 2009, 11:59:54 am »
Hey guys wud b glad if u cud help me with these sums

find the least 2 +ve values of @...

1)sin(2@+60)=0.3584
2)sin(30-@)=0.5
3)cos(3@-120)=0






  
 


« Last Edit: September 03, 2009, 12:02:51 pm by spiderman »
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master786

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Re: AS Math queries
« Reply #1 on: September 03, 2009, 12:26:16 pm »
wat are the limits ?
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Offline spiderman

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Re: AS Math queries
« Reply #2 on: September 03, 2009, 12:57:15 pm »
there are no limits
we just need 2 find d 2 least positive values of @
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master786

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Re: AS Math queries
« Reply #3 on: September 03, 2009, 01:06:46 pm »
for the first sum is the answer 49.5 and 160.5 ?
if its right i will post the method .. :P
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Offline spiderman

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Re: AS Math queries
« Reply #4 on: September 03, 2009, 01:35:57 pm »
Yes it is right
pls cud u post the steps

Thanks in advance

cos(3@-120)=0

(3\theta-120)=cos-10

3\theta-120)=360-cos-10

3\theta-120)=360+cos-10

3\theta-120)=720-cos-10

3\theta-120)=720+cos-10

3\theta-120)=1080-cos-10

3\theta-120)=1080+cos-10


Then solve all thes. Each equation mean a new \theta
« Last Edit: September 03, 2009, 01:50:47 pm by astarmathsandphysics »
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master786

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Re: AS Math queries
« Reply #5 on: September 03, 2009, 01:41:31 pm »
sin(2@ + 60)=0.3584

sin-1(0.3584)=21.000 degrees

21 is the correspondance angle

nd now using the grid .... u will see tht 180-21 & 360+21fit .

180-21= 159
360+21 = 381

ur criteria was 2@+60
therefore 2@+60=159 & 2@+60 = 381

solve these to eqns nd u will end up with the answers
« Last Edit: September 03, 2009, 01:44:02 pm by master786 »
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Offline astarmathsandphysics

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Re: AS Math queries
« Reply #6 on: September 03, 2009, 01:44:07 pm »
Quote from: spiderman on September 03, 2009, 11:59:54 am
Hey guys wud b glad if u cud help me with these sums

find the least 2 +ve values of @...

1)sin(2@+60)=0.3584
2)sin(30-@)=0.5
3)cos(3@-120)=0


1)
2theta+60=sin-10.3584

2theta+60=180-sin-10.3584

2theta+60=360+sin-10.3584

2theta+60=540-sin-10.3584
and solve these 4 equations

2)sin(30-@)=0.5

30=\theta=sin-1(0.5)

30=\theta=sin-1(0.5)

180-30=\theta=sin-1(0.5)
« Last Edit: September 03, 2009, 01:46:43 pm by astarmathsandphysics »
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Offline spiderman

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Re: AS Math queries
« Reply #7 on: September 03, 2009, 01:45:23 pm »
Thank you
Master786 and astar
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master786

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Re: AS Math queries
« Reply #8 on: September 03, 2009, 01:48:31 pm »
glad we cud help :)
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Offline spiderman

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Re: AS Math queries
« Reply #9 on: September 03, 2009, 01:54:51 pm »
Find all the values of @ in the interval -180<=@<=180
1)4sin@=5cos@
2)2sin@=1/sin@


Pls help me wit these sums
Guys i really suck in trignometry...wud b glad if u cud post some sites which demonstrate how to solve the type of sums that cum in the as and a level papers..... :)
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nid404

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Re: AS Math queries
« Reply #10 on: September 03, 2009, 02:07:52 pm »
Quote from: spiderman on September 03, 2009, 01:54:51 pm
Find all the values of @ in the interval -180<=@<=180
1)4sin@=5cos@
2)2sin@=1/sin@


Pls help me wit these sums
Guys i really suck in trignometry...wud b glad if u cud post some sites which demonstrate how to solve the type of sums that cum in the as and a level papers..... :)

I'll answer the second one in a while
for the first 1
4sintheta/5costheta=1
u r aware of
sintheta/costheta= tan theta
so
4sintheta/5costheta=0.8tantheta
0.8tantheta=1
tan theta=1 / 0.8
theta= tan-1(1/ 0.8)
theta=51.3
and 51.3-180=-128.7

hope u got it
« Last Edit: September 03, 2009, 02:27:58 pm by nid404 »
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Offline spiderman

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Re: AS Math queries
« Reply #11 on: September 03, 2009, 02:12:57 pm »
Thanks a lot buddy
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nid404

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Re: AS Math queries
« Reply #12 on: September 03, 2009, 02:16:12 pm »
second 1
2sin theta=1/sin theta
2=1/sin2theta
2sin2theta=1
sin2theta=1/2
sin theta= root of 1/2
theta= sin-1(1/2)1/2
theta= 45
and 45-180=-135

hope this helps and sorry for the delay
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