Calculus question - involving trigonometry

[rshen5]

Homework Statement

Homework Equations

The Attempt at a Solution

i have no idea how to start

 

[tiny-tim]

welcome to pf!

hi rshen5! welcome to pf!

(have a theta: θ and a square-root: √ )

show us what you've tried, and where you're stuck, and then we'll know how to help …

start with part a ​

 

[rshen5]

you have any idea where the 8 came from ?

 

[tiny-tim]

you have any idea where the 8 came from ?

i expect it's written in tiny print on the light bulb …

get on with it! ​

 

[rshen5]

well.. i know I am completely wrong, cause i don't even know what "I" is..

 

[tiny-tim]

(you don't need to know what I is, you only need to know when it's a maximum! )

why are you bothering with Pythagoras?

you've found that AN = xsinθ, and you know that AN = 1

 

[HallsofIvy]

The problem tells you that "I" is the "illumination"- the intensity of the light at that point. However, as tinytim suggests, knowing the specific physical meaning of variables is not necessary to do the mathematics!

 

[tiny-tim]

… knowing the specific physical meaning of variables is not necessary to do the mathematics!

maths is so cool!

 

[lurflurf]

recall from elementary trigonometry that
1+cot(t)^2=csc(t)^2
you got a little carried away
you wrote AN=x sin(theta)
also AN=1 so x=csc(theta)=1/sin(theta)
you can write I in terms of theta by substituting x=csc(theta) into I
x^2=x^2cos(theta)^2+x^2sin(theta)^2
reduces to the un helpful
x^2=x^2
not x^2=2x^2+1

 

[rshen5]

Thank you thank you ~~
gee that was easy.. (what was i thinking)

but does anyone know how they actually got the equation? just curious