Trigonometric Graphs Flashcards

All 6 cards in this deck

What is the period of $y = \sin x$ and $y = \cos x$?

$360°$ — each graph repeats every $360°$.

What is the period of $y = \tan x$?

$180°$ — the graph repeats every $180°$.

For $0° \le x \le 360°$, where are the asymptotes of $y = \tan x$?

$x = 90°$ and $x = 270°$, where $\cos x = 0$ so $\tan x$ is undefined.

How do you find the value of a trigonometric ratio of an angle outside $0°$ to $360°$?
e.g. $\sin 400°$

1. Add or subtract $360°$ until the angle lies in $0°$ to $360°$: $400° - 360° = 40°$
2. The ratio is unchanged: $\sin 400° = \sin 40°$

How many solutions does $\sin x = k$ have in $0° \le x \le 360°$ when $0 < k < 1$?

Two — the line $y = k$ cuts the sine curve twice, at $\alpha$ and $180° - \alpha$.

True or false? $\cos(-\theta) = -\cos\theta$ for any angle $\theta$.

False. $\cos(-\theta) = \cos\theta$, because the graph of $y = \cos x$ is symmetrical about the $y$-axis.