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

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: spiderman on September 03, 2009, 11:59:54 am

Title: AS Math queries
Post by: 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
Title: Re: AS Math queries
Post by: master786 on September 03, 2009, 12:26:16 pm: wat are the limits ?
Title: Re: AS Math queries
Post by: spiderman on September 03, 2009, 12:57:15 pm: there are no limits
we just need 2 find d 2 least positive values of @
Title: Re: AS Math queries
Post by: master786 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
Title: Re: AS Math queries
Post by: spiderman 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 $\theta$
Title: Re: AS Math queries
Post by: master786 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
Title: Re: AS Math queries
Post by: astarmathsandphysics 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)
2 $theta+60$ =sin^-10.3584

2 $theta+60$ =180-sin^-10.3584

2 $theta+60$ =360+sin^-10.3584

2 $theta+60$ =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)
Title: Re: AS Math queries
Post by: spiderman on September 03, 2009, 01:45:23 pm: Thank you
Master786 and astar
Title: Re: AS Math queries
Post by: master786 on September 03, 2009, 01:48:31 pm: glad we cud help :)
Title: Re: AS Math queries
Post by: 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..... :)
Title: Re: AS Math queries
Post by: nid404 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
Title: Re: AS Math queries
Post by: spiderman on September 03, 2009, 02:12:57 pm: Thanks a lot buddy
Title: Re: AS Math queries
Post by: nid404 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