Is tan(x + π) = tan x?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $9.99Unlock all

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

Is tan(x + π) = tan x?

Explanation:
Tangent repeats every π, so adding π to the angle doesn’t change its value. Express tan(x+π) as sin(x+π)/cos(x+π). With sin(x+π) = -sin x and cos(x+π) = -cos x, you get tan(x+π) = (-sin x)/(-cos x) = sin x/cos x = tan x, provided cos x ≠ 0. So the equality holds for all x where tan x is defined (i.e., x ≠ π/2 + kπ).

Tangent repeats every π, so adding π to the angle doesn’t change its value. Express tan(x+π) as sin(x+π)/cos(x+π). With sin(x+π) = -sin x and cos(x+π) = -cos x, you get tan(x+π) = (-sin x)/(-cos x) = sin x/cos x = tan x, provided cos x ≠ 0. So the equality holds for all x where tan x is defined (i.e., x ≠ π/2 + kπ).

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy