Mathematics · Ch 4 — Inverse Trigonometric Functions

Graph of Cosine Function

4.4.1

Graph of Cosine Function

Table of values on $[0,2\pi]$ :

$x$ (rad)	$0$	$\tfrac{\pi}6$	$\tfrac{\pi}4$	$\tfrac{\pi}3$	$\tfrac{\pi}2$	$\pi$	$\tfrac{3\pi}2$	$2\pi$
$\cos x$	$1$	$\tfrac{\sqrt3}2$	$\tfrac1{\sqrt2}$	$\tfrac12$	$0$	$-1$	$0$	$1$

The graph (Fig. 4.10) begins at $(0,1)$ , FALLS from $1$ to $-1$ as $x$ runs from $0$ to $\pi$ , then RISES from $-1$ back to $1$ as $x$ runs from $\pi$ to $2\pi$ . Repeating this portion on either side of $[0,2\pi]$ gives the full graph over $\mathbb{R}$ , shown in Fig. 4.11. …

Figure 4.10Fig. 4.10 - Graph of y = cos x on the interval [0, 2pi], starting at (0, 1), decreasing to -1 at x = pi, and increasing back to 1 at x = 2pi.

Fig. 4.10 — Fig. 4.10 - Graph of y = cos x on the interval [0, 2pi], starting at (0, 1), decreasing to -1 at x = pi, and increasing back to 1 at x = 2pi.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. The curve starting at its maximum $(0,1)$ , falling to a minimum $-1$ near $x=\pi$ , and rising back to $1$ by $x=2\pi$ . …

Figure 4.11Fig. 4.11 - Graph of y = cos x for x in R, showing the periodic repetition of the [0, 2pi] cycle over [-4pi, 4pi]; one cycle is highlighted.

Fig. 4.11 — Fig. 4.11 - Graph of y = cos x for x in R, showing the periodic repetition of the [0, 2pi] cycle over [-4pi, 4pi]; one cycle is highlighted.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. The Fig. 4.10 cycle repeated indefinitely on both sides of the origin, each hump an exact copy shifted by a multiple of $2\pi$ . …

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