What is the period of the tangent function y = tan x?

Study for the NBCT Mathematics AYA Component 1 exam. Utilize flashcards and multiple-choice questions with detailed explanations for each question. Prepare efficiently for success in your teaching certification journey!

Multiple Choice

What is the period of the tangent function y = tan x?

Explanation:
The basic idea is what number P makes tan(x+P) equal to tan(x) for all x where the function is defined. For tangent, tan(x+π) equals tan x because tan(x) = sin x / cos x and using angle addition, sin(x+π) = -sin x and cos(x+π) = -cos x, so tan(x+π) = (-sin x)/(-cos x) = tan x. That shows the function repeats every π units. The graph also has vertical asymptotes at x = π/2 + kπ, so the distance between repeats is π, reinforcing the fundamental period. Therefore, the period is π.

The basic idea is what number P makes tan(x+P) equal to tan(x) for all x where the function is defined. For tangent, tan(x+π) equals tan x because tan(x) = sin x / cos x and using angle addition, sin(x+π) = -sin x and cos(x+π) = -cos x, so tan(x+π) = (-sin x)/(-cos x) = tan x. That shows the function repeats every π units. The graph also has vertical asymptotes at x = π/2 + kπ, so the distance between repeats is π, reinforcing the fundamental period. Therefore, the period is π.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy