19.2: Ejercicios

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Page ID: 117695

Thomas Tradler and Holly Carley
CUNY New York City College of Technology via New York City College of Technology at CUNY Academic Works

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Ejercicio$\PageIndex{1}$

Grafica la función con la calculadora. Usa el modo radián y grado para mostrar tu gráfica. Haga zoom a una ventana apropiada para cada modo para mostrar una gráfica que incluya las características principales de la gráfica.

$y=\sin^{-1}(x)$
$y=\cos^{-1}(x)$
$ y=\tan^{-1}(x)$

Contestar

$clipboard_e4c73a7e5ee509f3cac908fdd712db817.png$ $\begin{aligned}&-2 \leq x \leq 2 \\&-2 \leq y \leq 2\end{aligned}$
$clipboard_ec15b01d8fc10b8828825274f03238602.png$ $\begin{aligned}&-2 \leq x \leq 2 \\&-1 \leq y \leq 4\end{aligned} $
$clipboard_e8d1a15881b5138fab8bbb49f7cdde065.png$ $\begin{aligned}-10 & \leq x \leq 10 \\-2 & \leq y \leq 2\end{aligned} $

Ejercicio$\PageIndex{2}$

Encuentra el valor exacto de la función trigonométrica inversa.

$\tan^{-1}(\sqrt{3})$
$\sin^{-1}\left(\dfrac{1}{2}\right)$
$\cos^{-1}\left(\dfrac{1}{2}\right)$
$\tan^{-1}(0)$
$\cos^{-1}\left(\dfrac{\sqrt{2}}{2}\right)$
$\cos^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)$
$\sin^{-1}(-1)$
$\tan^{-1}(-\sqrt{3})$
$\cos^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)$
$\sin^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)$
$\sin^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)$
$\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right)$

Contestar

$\dfrac{\pi}{3}$
$\dfrac{\pi}{6}$
$\dfrac{\pi}{3}$
$0$
$\dfrac{\pi}{4}$
$\dfrac{3\pi}{4}$
$-\dfrac{\pi}{2}$
$-\dfrac{\pi}{3}$
$\dfrac{5 \pi}{6}$
$-\dfrac{\pi}{4}$
$-\dfrac{\pi}{3}$
$-\dfrac{\pi}{6}$

Ejercicio$\PageIndex{3}$

Encuentra el valor de la función trigonométrica inversa usando la calculadora. Aproxime su respuesta a la centésima más cercana.

Para las partes (a) - (f), escribe tu respuesta en modo radián.

$\cos^{-1}(0.2)$
$\sin^{-1}(-0.75)$
$\cos^{-1}\left(\dfrac{1}{3}\right)$
$\tan^{-1}(100,000)$
$\tan^{-1}(-2)$
$\cos^{-1}(-2)$

Para las partes (g) - (l), escribe tu respuesta en modo grado.

$\cos^{-1}(0.68)$
$\tan^{-1}(-1)$
$\sin^{-1}\left(\dfrac{\sqrt{2}+\sqrt{6}}{4}\right)$
$\tan^{-1}(100,000)$
$\cos^{-1}\left(\dfrac{\sqrt{2-\sqrt{2}}}{2}\right)$
$\tan^{-1}(2+\sqrt{3}-\sqrt{6}-\sqrt{2})$

Contestar

$1.37$
$−0.85$
$1.23$
$1.57$
$−1.11$
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$47.16^{\circ}$
$-45^{\circ}$
$75^{\circ}$
$90.00^{\circ}$
$67.5^{\circ}$
$-7.5^{\circ}$

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Ejercicio\(\PageIndex{1}\)

Ejercicio\(\PageIndex{2}\)

Ejercicio\(\PageIndex{3}\)