• Best of luck to the class of 2019 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • Like us on facebook here

New questions (1 Viewer)

currysauce

Actuary in the making
Joined
Aug 31, 2004
Messages
576
Location
Sydney
Gender
Male
HSC
2005
A picture 2 metres high is hung on a wall with its bottom edge 6 metres above the eye of the viewer. How far from the wall should the viewer stand for the picture to subtend the largest possible verticle angle with her eye.

2.

Show that cosecx restricted to 0 < x < = pi/2 has an inverse (DONE). Calculate the inverse's derivative (that part)

thanks!
 
Last edited:

Sober

Member
Joined
Dec 6, 2005
Messages
215
Gender
Male
HSC
2003
tutor01 said:
Here is my solution. See attached.
I found this way easier.

Let x be the distance from the viewer to the wall and arctan represent inverse tan.

Angle of the picture = y = arctan(8/x) - arctan(6/x)

Let a=arctan(8/x) and b=arctan(6/x)

tan(y) = tan(a-b)

= [ tan(a) - tan(b) ] / [ 1 + tan(a).tan(b) ]

= [ (8/x) - (6/x) ] / [ 1 + (48/x^2) ]

= 2x / (x^2 + 48)

y = arctan( 2x / [x^2 + 48] )

Since arctan is an always increasing function it will be at a maximum when the argument is at a maximum so we need to find the max of:

z = 2x / [x^2 + 48]

z' = ( 2x^2 + 96 - 4x^2 ) / (x^2 + 48)^2

-2x^2 + 96 = 0

x =+ sqrt(48)

There is a maxiumum when x=sqrt(48)
 
Last edited:

Raginsheep

Active Member
Joined
Jun 14, 2004
Messages
1,227
Gender
Male
HSC
2005
Asking year12s to do a uni maths question (even though its "based on ext1 work) is poor effort mate :p
 

tutor01

Member
Joined
Jul 21, 2005
Messages
44
Gender
Male
HSC
N/A
I agree Sober - that is simpler for Question One. Of course both ways are valid solutions. Raginsheep - what uni Maths course has those sort of questions? I want the easy credit!
 

Raginsheep

Active Member
Joined
Jun 14, 2004
Messages
1,227
Gender
Male
HSC
2005
It comes from the calculus problem set for MATH1151 at unsw for actuary and finance/maths students. Its technically not uni work, just something to tie us over until we've covered enough to start on the "real" uni maths problems but still, point stands :D
 

currysauce

Actuary in the making
Joined
Aug 31, 2004
Messages
576
Location
Sydney
Gender
Male
HSC
2005
thanks guys, its easy now that i think about it...

hey sorry, its been awhile since i have done this stuff... i need a refresher haha. meh

thanks again
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top