Question

If tan(t)=57, what is tan(t-π)?
a) -57
b) 57
c) -tan(t)
d) tan(t)

Answer 1

Given that
`tan(t)=57` the value of
`tan(t-π)` is
`-57`, considering the properties of the tangent function's periodicity and its odd nature.

Step-by-step explanation:

To determine the value of tan(t-π) given that
`tan(t)=57`, we can use the periodic properties of the tangent function. The tangent function has a period of π which means that
`tan(θ) = tan(θ ± nπ)` for any integer n. Therefore
`tan(t-π) = tan(t)` because subtracting
`π` from t is equivalent to moving one full period along the tangent function.

However it is also important to recognize that the tangent function, while periodic, is odd. This fact means that
`tan(-θ) = -tan(θ)`. When subtracting
`π` from t in
`tan(t-π)`, we are essentially finding the tangent of the angle that is π radians less than t which is equivalent to finding the tangent of
`-t`. Therefore,
`tan(t-π) = -tan(t) = -57`.