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

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Igcseboy on April 29, 2010, 01:14:19 pm

Title: c2 DOUBT
Post by: Igcseboy on April 29, 2010, 01:14:19 pm: Jan 2007 question 9 c

and June 2007 question 9 a and b

They are from edexcel mathmetics C2

anyones help will be apprecited

thanxxx
Title: Re: c2 DOUBT
Post by: Saladin on April 29, 2010, 01:19:28 pm: In 30 minutes.
Title: Re: c2 DOUBT
Post by: astarmathsandphysics on April 30, 2010, 12:22:16 am: When i get up
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 09:38:08 am: could someone please solve this:

simplify the expression:

sin^4 thita + 2sin^2 thita cos^2 thita + cos^4 thita
Title: Re: c2 DOUBT
Post by: SGVaibhav on April 30, 2010, 09:45:03 am: do u mean this

USING X instead of thita
$sin^4(x) + 2sin^2(x)cos^2(x) + cos^4(x)$
Title: Re: c2 DOUBT
Post by: Saladin on April 30, 2010, 09:48:08 am: It is simply
$(sin^2\theta+cos^2\theta)^2$
Title: Re: c2 DOUBT
Post by: SGVaibhav on April 30, 2010, 09:52:18 am: Quote from: Mr. Enigmatic on April 30, 2010, 09:48:08 am
It is simply
$(sin^2\theta+cos^2\theta)^2$

which is equal to 1 =)
Title: Re: c2 DOUBT
Post by: Saladin on April 30, 2010, 09:56:35 am: I was getting to that :P
Title: Re: c2 DOUBT
Post by: SGVaibhav on April 30, 2010, 09:58:01 am: Solving Again

Question is
$sin^4\theta+ 2(sin^2\theta cos^2\theta)+cos^4\theta$

Which is equal to
$(sin^2 \theta + cos^2 \theta )^2$

And the identity
$sin^2\theta+cos^2\theta = 1$

Therefore the Answer is
$(1)^2 = 1$

=)
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 10:28:33 am: yes thankyou both very much :)
could u please solve this too:
find:
sin (x) and cos(x) , given that tan (x)=5/12 and that (x) is acute

thx
Title: Re: c2 DOUBT
Post by: astarmathsandphysics on April 30, 2010, 10:33:43 am: tan x =5/12 =o/a
h=sqrt(o^2 +a^2)=sqrt(5^2+12^2)=13
cos x=a/h =12/13
sin x= o/h=5/13
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 10:39:06 am: Quote from: astarmathsandphysics on April 30, 2010, 10:33:43 am
tan x =5/12 =o/a
h=sqrt(o^2 +a^2)=sqrt(5^2+12^2)=13
cos x=a/h =12/13
sin x= o/h=5/13

thx :)
Title: Re: c2 DOUBT
Post by: astarmathsandphysics on April 30, 2010, 11:22:04 am: no probs. so many asking questions atm. I will be here for next few hours at least.
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 12:16:02 pm: solve the equations for thita. in the interval 0<thita<360 :
sin thita + cos thita=0
Title: Re: c2 DOUBT
Post by: astarmathsandphysics on April 30, 2010, 12:32:51 pm: Take cos theta to the right and divide by cos theta to get tan theta=-1 so theta =-45 the keep adding 180 to get 135 and 315
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 01:06:13 pm: another questions:

solve the following equations for thita ,in the interval 0<thita<360
(sin thita - 1)(5 cos thita + 3)

solve the following equations for x:

cos x= -0.809, -180<x<180

the x value here is= 144, how do we find the rest of the solutions using the diagram method???
Title: Re: c2 DOUBT
Post by: astarmathsandphysics on April 30, 2010, 01:30:38 pm: is the 1st an equation
for the second equation do 360 -theta

http://www.astarmathsandphysics.com/a_level_maths_notes/C3/a_level_maths_notes_c3_finding_multiple_solutions_of_trigonometric_equations.html
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 01:53:49 pm: Quote from: astarmathsandphysics on April 30, 2010, 01:30:38 pm
is the 1st an equation
for the second equation do 360 -theta

http://www.astarmathsandphysics.com/a_level_maths_notes/C3/a_level_maths_notes_c3_finding_multiple_solutions_of_trigonometric_equations.html

yep the first is an equation which is equal to 0
Title: Re: c2 DOUBT
Post by: astarmathsandphysics on April 30, 2010, 02:26:38 pm: Phen put each bracket=0 and solve like in the link
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 04:08:04 pm: ok thx ;D ;D ;D ;D ;D
could u please tell me how to solve such questions ?:
find the values of thita, in the interval 0<thita<360 :
tan(45- thita)=-1

this is my method
let 45-thita = Z
but then how do i find the range for "Z" ???
thx aloooottt
Title: Re: c2 DOUBT
Post by: Saladin on April 30, 2010, 04:27:35 pm: $tan(45-x)=-1$

Therefore, $arctan(-1) = -45$

This can also mean that $arctan(-1)$ is $135$ and $315$ .

Thus, the only answer that is between 0 and 360 is $90$ .
Title: Re: c2 DOUBT
Post by: Saladin on April 30, 2010, 04:30:51 pm: Please note that arctan is just tan^-1
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 05:13:59 pm: Quote from: Mr. Enigmatic on April 30, 2010, 04:30:51 pm
Please note that arctan is just tan^-1

its 90 and 270 actually
thx but ;)
Title: Re: c2 DOUBT
Post by: halosh92 on April 30, 2010, 05:46:47 pm: cos(50 + 2 thita)=-1

??? how to find thita?
Title: Re: c2 DOUBT
Post by: Saladin on April 30, 2010, 06:18:41 pm: The answer is 65 and 245.

Work out the value of $cos(x)=-1$

Then you get 180.

So, $2x+50=180$

Now you get $65$

Now, just do $180+65$ , because you want a negative value. Cos will be negative in this quadrant.

And u get $245$