rshen5
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Calculus question - involving trigonometry
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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 …
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
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you have any idea where the 8 came from ?
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rshen5 said:
i expect it's written in tiny print on the light bulb
…get on with it! 
rshen5
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(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
)why are you bothering with Pythagoras?
you've found that AN = xsinθ, and you know that AN = 1
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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!
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HallsofIvy said:
maths is so cool!
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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
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
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