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Tuesday, October 9, 2012

problem on trigonometry

start from the LHS
use the formula for cos2x and sin2x

factorise the numerator
adjust the 1 in the denominator using trigonometry identity
write as a square

divide with sinx to change to cot x


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Wednesday, October 3, 2012

integral of arc (sin x)

integral of arc (sin x) using integration by parts

change to arc (sin x) . 1 and use integration by parts with

u = arc(sin x)  and v =1


formulae on integration
 
PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

 PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR


PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

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Monday, June 11, 2012

first year b tech math exam of kerala university

The first year btech math exam of kerala university that was postponed earlier is likely to be conducted on wednesday the 13th of june 2012. Most students who wasted almost one and a half weeks due to the 3 postponed exams have just one day to go through the whole math portion because they seem to have had some other university exam on monday . Students from loyola school are very excited about their cultural event called la fest which is to take place later this month. Today I went a shop to buy some mats made of waste cotton. The shop keeper asked for Rs.30/- per mat. (The same mats used to cost around Rs.10/- to Rs. 15/- just a couple of years ago ).Household wiring equipment like switches and powerplugs with a few metres of thick guage wire, plastic pipes etc cost around Rs. 1000/-. Almost the same quantity of material used to cost around 700 rupees just a year back . A doctor adviced a patient to regularly incorporate leafy vegetables like cheere, cabbage and fruits like palayankodan (a variety of plantain)to avoid constipation and painful bowel movements . The palayankodan variety used to cost around 18 to 20 rupees a kilo while the rasakadhaly variety used to cost somewhere between 32 to 40 rupees a kilo .But now some shopkeepers are charging around 25 rupees for a kilo of palauankodan variety. But for ripe mangoes, around march, some varieties used to cost around 150 to 200 rupees per kg. But in the last week of may the same varieties cost only around 40 to 60 rupees per kg.
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Thursday, June 7, 2012

kyc norms for mutual fund investment

Yesterday I had gone to the cams office near lic office near the government girls higher secondary school at pattom to ask about the kyc norms for mutual fund investment for my wife. The person at the counter in the cams office asked if my wife already had some old mutual fund investments in her name. They asked for a investment into some mutual fund handled by cams to accompany the kyc nomination form, since she did not have any old folio number in her name. So I went today with the kyc application form, pan card attested copy, proof of address, and a cheque for a small investment into a mutual fund by sbi mutual fund amc along with the application for the mutual fund. They accepted the forms. Then I went to the state bank of india, pattom branch which is close to the cams office. I wanted to update a pass book. There is a separate counter for updating the pass book in that branch, but the new line of update was overwritten on an already printed line. The person at the counter had to print all the entries on that page onto a new page for the entries to be legible. There is a Spencer's outlet just below the sbi office. I went there to buy some uzhunnu (urad dhal) and dopi rice used for making idlis and dosas. The ratio is about 1:4. Half a kilo of urad dhal cost about 39 rupees and two kilos of dopi rice cost about 54 rupees. A kilo of kera coconut oil cost about 85 rupees. I also wanted to buy some dried red chillies and some jeerakam.The red chillies was only availabe in bigger packets (for powdering I guess). The funny thing was jeerakam was also packed into big packets costing around 150 rupees or something. So I had to go the more outlet at marappalam junction. There I bought around 100 grams of dried red chilly for about 20 rupees (slightly exorbitant i guess) .There were smaller packets of jeerakam in this shop. I also bought a 5 kilo packet of ponni rice for around 135 rupees. One drawback of this shop is that the staff in the counter never seeem to have any change( they always seem to run out of 100 rupee, 50 rupee and even 10 rupee notes all the time).
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Monday, May 21, 2012

cbse class X exam result for chennai region

cbse class X (class 10) exam result for chennai region has been announced . It is available at http://cbseresults.nic.in/
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Saturday, February 11, 2012

if A+B+C = 180° , show that cot A cotB + cotBcotC +cotC cotA=1

if A+B+C = 180° ,
show that

tanA +tanB + tanC = tanAtanBtanC and

cot A cotB + cotBcotC +cotC cotA=1



given A+B+C = 180°

implies A + B = 180°- C

implies tan(A + B) = tan(180°- C)

using trigonometry formulae

tan(A + B) = -tan(C)

therefore

[tanA +tanB] / [1-tanAtanB ] = -tanC

cross multiplying

tanA +tanB = -tanC[1-tanAtanB ]

tanA +tanB = -tanC +tanAtanBtanC

or

tanA +tanB + tanC = tanAtanBtanC

divide each term with tanAtanBtanC we get


cot A cotB + cotBcotC +cotC cotA=1

some other problems
If A+B+C=π,
prove that: sinA+sinB+sinC = cot(A/2).cot(B/2) [sinA+sinB-sinC]

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Saturday, February 4, 2012

some useful symbols

≡ ~
± ∓
∤ ◅
∈ ∉
⊆ ⊂ ∪ ∩ ⊥ ô





·
∫ Σ → ∞
Π Δ Φ Ψ Ω Γ ∮ ∇∂ √ ∅ °
α β γ δ ε ζ η θ
ι κ λ μ ν ξ ο π
ρ σ τ υ φ χ ψ ω x²
some interesting symbols for posting into forums.


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Friday, January 20, 2012

confidence interval

confidence interval for population proportion (P) is

( p - (z)sqrt(pq/n) , p + (z)sqrt(pq/n) )

where z is the table value corresponding to the required confidence level, (two tailed)
p the sample proportion , q = 1 - p
n = sample size

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Thursday, January 19, 2012

inverse and direct variation

u is said to be directly proportional to v if u = c v for some constant c

u is said to be inversely proportional to v if u = [k / v] for some constant k

In direct variation, u increases as v increases and vice versa.

In inverse variation, u decreases as v increases and vice versa.


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Monday, January 2, 2012

problem of splitting into real and imaginary parts

if u+iv = (x +iy) ^3 , show that (u/x) + (v/y) = 4( x² -y² )

first expand (x +iy) ^3 using binomial expansion or identity and then split into real and imaginary parts then manipulate


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