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

Qualification => Reference Material => GCE AS & A2 Level => Revison Notes => Topic started by: nid404 on August 01, 2010, 02:24:08 pm

Title: Trigonometry
Post by: nid404 on August 01, 2010, 02:24:08 pm: $sec x=$ $\frac{1}{cosx}$ provided cosx is not equal to 0

$cosec x=$ $\frac{1}{sinx}$ provided sinx is not equal to 0

$cot x=$ $\frac{cosx}{sinx}$ provided sinx is not equal to 0

$cot x=$ $\frac{1}{tanx}$ provided tanx is not equal to 0

1) $cos^2x + sin^2x= 1$

divide by cos²x

$\frac{cos^2x + sin^2x= 1}{cos^2x}$

$1+ tan^2x=sec^2x$

2) $cos^2x + sin^2x= 1$

divide by sin²x

$\frac{cos^2x + sin^2x= 1}{sin^2x}$

$cot^2x+1=cosec^2x$
Title: Re: Trigonometry
Post by: DrEvil on August 01, 2010, 02:34:46 pm: Aren't these written in the books too? :-\
Title: Re: Trigonometry
Post by: nid404 on August 01, 2010, 02:36:13 pm: Quote from: DrEvil on August 01, 2010, 02:34:46 pm
Aren't these written in the books too? :-\

yeah...but one of the members asked me to explain with steps and solve a few problems on it :)
Title: Re: Trigonometry
Post by: DrEvil on August 01, 2010, 02:41:16 pm: Quote from: ~Ahana~ on August 01, 2010, 02:36:13 pm
yeah...but one of the members asked me to explain with steps and solve a few problems on it :)

That's okay... I was just asking because it takes a lot of hard work and time to write all these.
Title: Re: Trigonometry
Post by: nid404 on August 01, 2010, 02:42:12 pm: Quote from: DrEvil on August 01, 2010, 02:41:16 pm
That's okay... I was just asking because it takes a lot of hard work and time to write all these.

Naah...it's fine...It's revision for me ;)
Title: Re: Trigonometry
Post by: nid404 on August 01, 2010, 03:09:00 pm: Ex 5 A

2) a)sec (1/2pi -x)

= 1/ cos (1/2pi -x)

cos(1/2 pi-x)=sin x

so 1/cos(1/2pi-x)=1/sinx = cosec x

f) cosec (pi + x)

=1/sin(pi+x)

sin(pi+x)= -sin x

1/-sin x= -cosec x

3) c) cot 5/6 pi

=1/tan 5/6pi

= 1/-1/ $\sqrt3$

=- $\sqrt3$

e) cot(-1/3pi)

1/ tan(-1/3 pi)

= 1/- $\sqrt3$

5) b) cot A= 1/tan A

tan A= sin A/cos A

1/tan A= cos A/sin A

1/tan A= (4/5)/ (3/5)= 4/3

d) cosecB = 1/sin B

sin= $\sqrt3$ / 2

cosecB= 2/ $\sqrt 3$ = 2 $\sqrt3$ /3
Title: Re: Trigonometry
Post by: nid404 on August 01, 2010, 03:28:10 pm: Additional formulae

cos(A-B)=cosAcosB+sinAsinB
cos(A+B)=cosAcosB-sinAsinB
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)= sinAcosB-cosAsinB

tan(A+B)= $\frac{tanA+tanB}{1-tanAtanB}$

tan(A-B)= $\frac{tanA-tanB}{1+tanAtanB}$

Ex 5B

2)

a) cos 105^o

cos (60+45) = cos60.cos45- sin60.sin45
=1/2. 1/ $\sqrt2$ - $\sqrt3$ /2. 1/ $\sqrt2$
=1/2 $\sqrt2$ - $\sqrt3$ /2 $\sqrt2$
= 1-3/ 2 $sqrt2$
= $\sqrt2$ - $\sqrt6$ / 4

4) sin(3/2pi + x)

= sin3/2picosx+ cos3/2pisinx
=-1cosx+0sinx
=-1cosx
Title: Re: Trigonometry
Post by: nid404 on August 01, 2010, 03:36:52 pm: Double angle formulae

sin (A+B)= sinAcosB+cosAsinB

when A=B

sin (A+A)= sinAcosA+cosAsinA
sin 2A= 2cosAsinA

cos(A+B)=cosAcosB-sinAsinB
when A=B
cos 2A= cosAcosA-sinAsinA
cos2A=cos²A- sin²A

cos 2A in terms of sin²A

cos²A+ sin²A=1
cos²A=1-sin²A

cos2A= 1-sin²A-sin²A
=1-2sin²A

in terms of cos²A

cos2A= cos²A-(1- cos²A)
=2cos²A-1

tan(A+B)= $\frac{tanA+tanB}{1-tanAtanB}$

if A=B

tan 2A= $\frac{2tanA}{1-tan^2x}$
Title: Re: Trigonometry
Post by: nid404 on August 01, 2010, 04:46:48 pm: 5C

3) sin 3A

sin (2A+A)= sin2AcosA+cos2AsinA
sin2A=2cosAsinA and cos2A= 1-2sin²A
sin3A= 2cosAsinAcosA + 1-2sin²AsinA
sin3A=2(1-sin²A)sinA+ sinA- 2sin³A
sin3A= 2sinA-2sin³A+sinA-2sin³A
sin3A=3sinA-4sin³A

8)tan 2A= 12/5
tan 2A= 2tanA/1-tan²A
12/5=2tanA/1-tan²A

12-12tan²A=10tanA
-12tan²A-10tanA+12=0

let tanA=x

-12tan²x-10tanx+12=0

solve quadratic

x=-1.5 and 2/3

thus tan A= -1.5 and 2/3
Title: Re: Trigonometry
Post by: shedow_21 on August 09, 2010, 04:53:35 am: :o Did you learned all that......
Title: Re: Trigonometry
Post by: nid404 on August 16, 2010, 02:43:29 pm: Quote from: shedow_21 on August 09, 2010, 04:53:35 am
:o Did you learned all that......

Do I have a choice? :P
Title: Re: Trigonometry
Post by: Saladin on August 18, 2010, 01:14:37 pm: Guys, you can find all these formulas and more in this document:

Here (http://www.edexcel.com/migrationdocuments/GCE%20New%20GCE/N38210A-GCE-Mathematical-Formulae-Statistical-Tables.pdf)
Title: Re: Trigonometry
Post by: @d!_†oX!© on August 23, 2010, 06:45:46 pm: Quote from: Engraved on August 18, 2010, 01:14:37 pm
Guys, you can find all these formulas and more in this document:

Here (http://www.edexcel.com/migrationdocuments/GCE%20New%20GCE/N38210A-GCE-Mathematical-Formulae-Statistical-Tables.pdf)

this one's edexcel..i know it does not mae much of a difference but could see if you have the formula sheet for CIE Pure Mathematics..its called MF9
Title: Re: Trigonometry
Post by: cooldude on August 23, 2010, 06:46:54 pm: Quote from: @d!_†oX!© on August 23, 2010, 06:45:46 pm
this one's edexcel..i know it does not mae much of a difference but could see if you have the formula sheet for CIE Pure Mathematics..its called MF9

open the syllabus, its on the last few pages
Title: Re: Trigonometry
Post by: @d!_†oX!© on August 23, 2010, 06:53:30 pm: Quote from: cooldude on August 23, 2010, 06:46:54 pm
open the syllabus, its on the last few pages

Thanks