True or false?
tan x = tan(x-6pi)
Sona really just copied Reiny like that
Using tan(A-B) = (tanA - tanB)/(1+tanAtanB)
RS = tan(x-6π)
= (tanx - tan 6π)/(1 + tanxtan 6π)
but 6π is coterminal with 2π (6π is 3 rotations, and 2π is one rotation
so tan 6π = tan 2π = 0
= (tanx - 0)/(1+ ) = tanx = LS
so the statement is true
or
tan(-A) = -tanA
so tan(x-6π) = - tan(6π-x)
= -tan(2π-x) , since 6π is coterminal with 2π
= -( -tan(x) ) , by the CAST rule
= tanx
the statement is true
Using tan(A-B) = (tanA - tanB)/(1+tanAtanB)
RS = tan(x-6π)
= (tanx - tan 6π)/(1 + tanxtan 6π)
but 6π is coterminal with 2π (6π is 3 rotations, and 2π is one rotation
so tan 6π = tan 2π = 0
= (tanx - 0)/(1+ ) = tanx = LS
so the statement is tru
False. In general, tan(x) = tan(x+2nπ) for any integer n, but not for tan(x-6π). It's like trying to find your way back to the same joke that was told 6 hours ago at the circus. It just won't work!
To determine if the statement "tan x = tan(x-6pi)" is true or false, we need to apply the trigonometric property known as the period of the tangent function.
The tangent function has a period of π. This means that the value of tan(x) repeats every π units. In other words, tan(x) = tan(x + π).
In the given equation, tan x = tan(x-6pi), note that the difference between x and (x-6pi) is 6π. Since the period of the tangent function is π, we can write 6π as a multiple of π.
6π = 6 * π
Therefore, the equation can be simplified as:
tan x = tan(x + 6π)
Because the value of x + 6π is equivalent to x due to the periodic nature of the tangent function, we can conclude that the statement is true:
tan x = tan(x-6pi) is true.