Find the exact value of the following expression, if possible.
tan-1 (tan 2π/3)
I need help with this problem. Correct answer gets 10 points.
2007-10-24 10:09:58 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
= tan ^(-1) ( -√3) = 2π / 3
2007-10-28 08:31:06 · answer #1 · answered by Como 7 · 0⤊ 0⤋
Short blurb on inverse functions:
Say you have a function f(x). Its inverse is denoted by f(-1)(x) (in a textbook the "-1" appears as a superscript).
So then if you do something like f( f(-1)(x) ), the function and its inverse cancel each other out and you are left with x
tan-1 is the inverse of tan
therefore the function and its inverse cancel each other out and you are left with 2π/3
tan-1 (tan 2π/3) = 2π/3
2007-10-24 10:17:21 · answer #2 · answered by Dana N 1 · 0⤊ 0⤋
tan^-1 (tan θ) = θ, but only if -π/2 < θ < π/2.
Use the fact that tangent is periodic with period π, that tan(θ) = tan(θ + k*π) for any integer k to change
tan 2π/3 = tan (2π/3 - π) = tan (-π/3).
Your answer is -π/3.
2007-10-24 10:22:20 · answer #3 · answered by ♣ K-Dub ♣ 6 · 0⤊ 0⤋