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Author Topic: Trigonometry  (Read 3663 times)

nid404

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Trigonometry
« 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




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Offline DrEvil

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Re: Trigonometry
« Reply #1 on: August 01, 2010, 02:34:46 pm »
Aren't these written in the books too?  :-\
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nid404

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Re: Trigonometry
« Reply #2 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  :)
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Offline DrEvil

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Re: Trigonometry
« Reply #3 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.
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nid404

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Re: Trigonometry
« Reply #4 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  ;)
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nid404

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Re: Trigonometry
« Reply #5 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
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nid404

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Re: Trigonometry
« Reply #6 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 105o

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

4)  sin(3/2pi + x)

= sin3/2picosx+ cos3/2pisinx
=-1cosx+0sinx
=-1cosx
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nid404

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Re: Trigonometry
« Reply #7 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}

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nid404

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Re: Trigonometry
« Reply #8 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
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Offline shedow_21

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Re: Trigonometry
« Reply #9 on: August 09, 2010, 04:53:35 am »
 :o Did you learned all that......
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nid404

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Re: Trigonometry
« Reply #10 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
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Offline Saladin

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Re: Trigonometry
« Reply #11 on: August 18, 2010, 01:14:37 pm »
Guys, you can find all these formulas and more in this document:

Here
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Offline @d!_†oX!©

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Re: Trigonometry
« Reply #12 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

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
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Offline cooldude

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Re: Trigonometry
« Reply #13 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
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Offline @d!_†oX!©

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Re: Trigonometry
« Reply #14 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
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