The values of t for which the function is not defined are:
t = 1/4, 3/4, 5/4, 7/4
How to find the values where it is not-defined?
Ok, we have the function:
d = 10*tan(2πt)
We can rewrite it as a quotient between a sine and a cosine, then we can write:
d = 10*sin(2πt)/cos(2πt)
We can't divide by zero, so we need to remove the values of t such that:
cos(2πt) = 0
We know that:
cos(π/2) = cos(3π/2) = cos(π/2 + n*2π) = cos(3π/2 + n*2π) = 0
So:
if
2πt = π/2
t = 1/4 --> must be removed.
if 2πt = 3π/2
t = 3/4 ---> must be removed.
Then it happens again when:
if 2πt = 5π/2
t = 5/4 ---> must be removed.
And finally:
if 2πt = 7π/2
t = 7/4 ---> must be removed.
For these values of t, the function is not defined because the denominator becomes zero.
Complete question:
"An ambulance with a rotating beam of light is parked 10 feet from a building. The function d = 10 tan(2πt) describes the distance the rotating beam of light from point C after t seconds.
Find the values in [0, 2] where it is not defined"