Question

Express the illuminance on the floor as a composite function of t for 0 < t < 8.

Answer 1

The formula for illuminance is given by
E = I / d^2
This formula only holds true for one-dimensional illuminance
The problem asks for the illuminance across the floor. We need to use two variables, x and y.
From Pythagorean Theorem
d^2 = x^2 + y^2
and from Trigonometry
x = d cos t
y = d sin t

The function for the illuminance can be represented by the composite function
E = I cos² t / x²
and
E = I sin² t / y²

The boundary of these functions is:
0 < t < 8
So, the value of t must be in radians and not in degrees