Asadkarim7
  • Asadkarim7
the tangent and normal to the curve y= sin x at the point P where x= π/3 cut the x-axis at A and B respectively (a). show that AB = (5√3)/4. (b). find the area of the triangle PAB.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
the tangent to the curve is what..cos(pi/3) right?
amistre64
  • amistre64
the normal is 90 from that....
amistre64
  • amistre64
i dont quite understand the cuts the x axis at A and B

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anonymous
  • anonymous
maybe x and y axis at A and B?
amistre64
  • amistre64
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anonymous
  • anonymous
no
anonymous
  • anonymous
they mean the tangent cuts at a, and the normal cuts at b
Asadkarim7
  • Asadkarim7
let me post the digaram
anonymous
  • anonymous
its very simple find the eqns of the lines , find the intercepts of those lines , then use distance formula
amistre64
  • amistre64
lol.... yeah, if you post it that would be more helpful :)
amistre64
  • amistre64
simple yes, once you understand the question ;)
anonymous
  • anonymous
just distance formula and area of a triangle = (1/2) bh , thats all there is , you dont even need a picture for this, should be able to draw one yourself, or visualise in your mind pretty easily
Asadkarim7
  • Asadkarim7
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amistre64
  • amistre64
well the tangent is simply its derivative; cos(pi/3)
amistre64
  • amistre64
the equation of the line then becomes: y-(sin(pi/3)) = cos(pi/3)(x-(pi/3))
amistre64
  • amistre64
cos(pi/3) = 1/2 right?
amistre64
  • amistre64
the normal will have a slope of -2 then
amistre64
  • amistre64
y-(sin(pi/3)) = -2(x-(pi/3)) for the normal equation
Asadkarim7
  • Asadkarim7
Guys i still cant understand it , can sun1 explain it to me step by step ? plz
amistre64
  • amistre64
they give you a point (pi/3, sin(pi/3)); or rather (pi/3, sqrt(3)/2) right?
anonymous
  • anonymous
first take the derivative of sine, which is cosine. then plug in \[\frac{\pi}{3}\] into the derivative to get the slope. \[cos(\frac{\pi}{3})=\frac{1}{2}\] so that is the slope of the tangent line
amistre64
  • amistre64
at this level you should have some redimentary skills at a graph id assume :)
amistre64
  • amistre64
use the poit-slope form of a line to get the euation for the tangent and the norml
anonymous
  • anonymous
amistre is in right direction,find the eqn of tangent and normal to the curve, find the x intercepts of both to find out the coordiantes of the two points, point P is given, it forms the triangle ABP
amistre64
  • amistre64
someones been rearragnging my keyboard lol
anonymous
  • anonymous
the equation of the line use the point slope formula. the point is \[(\frac{\pi}{3},\frac{\sqrt{3}}{2})\] and the slope is \[\frac{1}{2}\] so the equation is \[y-\frac{\sqrt{3}}{2}=\frac{1}{2}(x-\frac{\pi}{3})\]
anonymous
  • anonymous
this crosses the x axis where \[y=0\] so set \[y=0\] and solve to get \[x=\frac{\pi}{3}-\sqrt{3}\] if i did the algebra right
anonymous
  • anonymous
repeat the process for the line with slope -2 through \[(\frac{\pi}{3},\frac{\sqrt{3}}{2})\]
amistre64
  • amistre64
x/2 - pi/6 = -sqrt.3/2 x = -sqrt3 + pi/3 its good ;)
anonymous
  • anonymous
amistre did i screw this up? it looks good to me
anonymous
  • anonymous
thnx
amistre64
  • amistre64
the normal just uses -2 for th eslope then
anonymous
  • anonymous
\[y-\frac{\sqrt{3}}{2}=-2(x-\frac{\pi}{3})\] is the normal line yes?
amistre64
  • amistre64
yes
anonymous
  • anonymous
let \[y=0\] get \[x=\sqrt{3}+\frac{\pi}{3}\]
anonymous
  • anonymous
at least that is what i got
amistre64
  • amistre64
/ -2 to begin with to ease the process
amistre64
  • amistre64
sqrt.3/4 + pi/3 i think
anonymous
  • anonymous
\[-\frac{\sqrt{3}}{2}=-2(x-\frac{\pi}{3})\] \[\sqrt{3}=x-\frac{\pi}{3}\] \[x=\sqrt{3}+\frac{\pi}{3}\]
anonymous
  • anonymous
whoooooooooooooooooops
anonymous
  • anonymous
lorda mercy
anonymous
  • anonymous
\[\frac{\sqrt{3}}{4}+\frac{\pi}{3}\]
anonymous
  • anonymous
another dumb guy award for me.
anonymous
  • anonymous
thnx
amistre64
  • amistre64
lol.... thats what all my medals are for ;)
anonymous
  • anonymous
ok fine. now that we have the x-intercepts, after some elementary algebra mistakes on my part, what are we supposed to do with them?
amistre64
  • amistre64
throw tham at moving trains :)
anonymous
  • anonymous
u both deserve for it :)
anonymous
  • anonymous
i forgot what we were supposed to do with these. multiply? add? find the length?
anonymous
  • anonymous
i mean for medals ;)..not throwing at the moving train :P
amistre64
  • amistre64
the distance between them is just large - small
anonymous
  • anonymous
now the final task, area of the triangle
amistre64
  • amistre64
since they are on the number line; distance between them is large - small
amistre64
  • amistre64
distance between 6 and -3 is 6--3 = 9 ;)
amistre64
  • amistre64
height = sqrt3/2 ; distance = l-s --------------------------- = area 2
anonymous
  • anonymous
meant to find an area lol but you guys have done it all over the place and its highly likely that the OP has just giving up on trying to follow what you guys have wrote
amistre64
  • amistre64
the journey taken is more important the the final destination....... grasshopper
amistre64
  • amistre64
sats been consistently and systematically finding the points... its good
anonymous
  • anonymous
ooh some arithmetic i can do! \[\frac{\sqrt{3}}{4}+\frac{\pi}{3}-(\frac{\pi}{3}-\sqrt{3})=\frac{\sqrt{3}}{4}+\sqrt{3}=\frac{5\sqrt{3}}{4}\]
anonymous
  • anonymous
wow just what it said it was!
anonymous
  • anonymous
very east to set out working out to make the solution of these questions look really easy instead of making it look so complicated with 1000s of posts etc.
anonymous
  • anonymous
true but very hard to type all in in one box. specially if typesetting.
amistre64
  • amistre64
depends on if you wanna read a novel or have a conversation type environment; there isnt only one way to do things :)
anonymous
  • anonymous
hi yo man
amistre64
  • amistre64
this type of environment is suited best for interaction between questioneer and answeer
amistre64
  • amistre64
if they really want a static read thru answer; theres always the internet lol
anonymous
  • anonymous
Asadkarim7 i will be happy to work all this out on one paper and send it to you if this is confusing. the idea is this: find the slope of the tangent line, then find its equation. find the slope of the normal line, and its equation. then in each equation set y = 0 and solve for x. that is the whole idea. once you have both x intercepts subtract to get the distance. the rest is mechanics, but i will be happy to write it out in all its gory details without my algebra errors if you like
amistre64
  • amistre64
asad is intelligent :)
anonymous
  • anonymous
i am sure he is but i will be happy to do it to practice my latex
anonymous
  • anonymous
make a pdf
amistre64
  • amistre64
:) latex.... i perfer ascii lol
Asadkarim7
  • Asadkarim7
thanks :P amistre64
anonymous
  • anonymous
luddite
anonymous
  • anonymous
^ "its very simple find the eqns of the lines , find the intercepts of those lines , then use distance formula" esessentially what I wrote like a whole hour ago
amistre64
  • amistre64
ohhh..... so everything after that is useless and should be erased becasue its just utter garbage? .... comes across a bit pompuos dontcha think ;)
amistre64
  • amistre64
in fact the "i still dont understand can you explain it to me step by step" kinda leads me to believe otherwise ... lol
anonymous
  • anonymous
also, geez, way to spam the question guys, nw my computer is going extremely slow when I view this particular question because you guys spammed it so much :|
amistre64
  • amistre64
youre prolly using internet explorer; i had to down firefox to avoid that
amistre64
  • amistre64
the equation editor stuff tends to put a strain on the processor; which is why i tend to avoid it
amistre64
  • amistre64
so asad; how can we help you with this problem?
anonymous
  • anonymous
here it is
1 Attachment
anonymous
  • anonymous
let me know if you have any questions
amistre64
  • amistre64
you forgot to put in the area lol
anonymous
  • anonymous
oh heavens. fine.
amistre64
  • amistre64
and here my fine useless garbage contribution ;)
1 Attachment
Asadkarim7
  • Asadkarim7
sattelite73 u made the equation y = sqrt 3/ 2 it should have been y- sqrt 3/2
anonymous
  • anonymous
\[\frac{1}{2}bh=\frac{1}{2}\times \frac{5\sqrt{3}}{4}\times \frac{\sqrt{3}}{2}=\frac{15}{16}\]
amistre64
  • amistre64
its his latex.... makes him go a little insane at times and starts putting = signs for - signs :)
anonymous
  • anonymous
everyone is a critic. ok that was a typo and look, it is gone!
1 Attachment
amistre64
  • amistre64
that ones just blank.....
Asadkarim7
  • Asadkarim7
u r genius sattelite 73
anonymous
  • anonymous
what lovely font! what nice equations!
anonymous
  • anonymous
how didi u make pdf file
anonymous
  • anonymous
eventually i will learn this latex ... eventually.
amistre64
  • amistre64
he starts out with some fine kindling, then adds a bit of tinder to feed the flame..
anonymous
  • anonymous
i am using texmaker as an editor. just converts for you if you ask, and then can ask for external viewer. really quite friendly. i tried to use this on micordemon windows whatever and it took me maybe a day and a half to download what i needed. miktex and all that garbage. never worked right. left the darkside for linux a few months ago, to maybe 2 minutes do download and works like a charm.
anonymous
  • anonymous
it is true i start with the trees. used to roll my own when i smoked. also doing html by hand if i can (with editor of course)
amistre64
  • amistre64
anonymous
  • anonymous
also spelled "point" and 'derivative' wrong. perils of not using wysiwyg
anonymous
  • anonymous
armistre will this make my computer explode?
amistre64
  • amistre64
1 Attachment
amistre64
  • amistre64
hopefully lol
anonymous
  • anonymous
this will keep me busy for at least an hour. click, click, ...
amistre64
  • amistre64
lol :)
Asadkarim7
  • Asadkarim7
Thanks Everyone for your contributions , and giving your precious time to my question <3
amistre64
  • amistre64
i made a 'flip book' javascript movie maker for my neices
amistre64
  • amistre64
youre welcome :) and thank you elec for making it all possible lol
anonymous
  • anonymous
welcome. hope it is clear enough even with all this garbage thrown in.
Asadkarim7
  • Asadkarim7
yeahh satellite its crystal clear . :)

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