19.2: Exercises

Precalculus · LibreTexts

0%

Contents

    Text

    Size
    100%
    Theme
    Typeface
    Line length
    Spacing

    From LibreTexts, under CC BY-NC-SA 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    Exercise \(\PageIndex{1}\)

    Graph the function with the calculator. Use both radian and degree mode to display your graph. Zoom to an appropriate window for each mode to display a graph which includes the main features of the graph.

    1. \(y=\sin^{-1}(x)\)
    2. \(y=\cos^{-1}(x)\)
    3. \( y=\tan^{-1}(x)\)
    Answer
    1. clipboard_e4c73a7e5ee509f3cac908fdd712db817.png \(\begin{aligned}&-2 \leq x \leq 2 \\&-2 \leq y \leq 2\end{aligned}\)
    2. clipboard_ec15b01d8fc10b8828825274f03238602.png \(\begin{aligned}&-2 \leq x \leq 2 \\&-1 \leq y \leq 4\end{aligned} \)
    3. clipboard_e8d1a15881b5138fab8bbb49f7cdde065.png \(\begin{aligned}-10 & \leq x \leq 10 \\-2 & \leq y \leq 2\end{aligned} \)

    Exercise \(\PageIndex{2}\)

    Find the exact value of the inverse trigonometric function.

    1. \(\tan^{-1}(\sqrt{3})\)
    2. \(\sin^{-1}\left(\dfrac{1}{2}\right)\)
    3. \(\cos^{-1}\left(\dfrac{1}{2}\right)\)
    4. \(\tan^{-1}(0)\)
    5. \(\cos^{-1}\left(\dfrac{\sqrt{2}}{2}\right)\)
    6. \(\cos^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)\)
    7. \(\sin^{-1}(-1)\)
    8. \(\tan^{-1}(-\sqrt{3})\)
    9. \(\cos^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\)
    10. \(\sin^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)\)
    11. \(\sin^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\)
    12. \(\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right)\)
    Answer
    1. \(\dfrac{\pi}{3}\)
    2. \(\dfrac{\pi}{6}\)
    3. \(\dfrac{\pi}{3}\)
    4. \(0\)
    5. \(\dfrac{\pi}{4}\)
    6. \(\dfrac{3\pi}{4}\)
    7. \(-\dfrac{\pi}{2}\)
    8. \(-\dfrac{\pi}{3}\)
    9. \(\dfrac{5 \pi}{6}\)
    10. \(-\dfrac{\pi}{4}\)
    11. \(-\dfrac{\pi}{3}\)
    12. \(-\dfrac{\pi}{6}\)

    Exercise \(\PageIndex{3}\)

    Find the inverse trigonometric function value using the calculator. Approximate your answer to the nearest hundredth.

    For parts (a)-(f), write your answer in radian mode.

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

    For parts (g)-(l), write your answer in degree mode.

    1. \(\cos^{-1}(0.68)\)
    2. \(\tan^{-1}(-1)\)
    3. \(\sin^{-1}\left(\dfrac{\sqrt{2}+\sqrt{6}}{4}\right)\)
    4. \(\tan^{-1}(100,000)\)
    5. \(\cos^{-1}\left(\dfrac{\sqrt{2-\sqrt{2}}}{2}\right)\)
    6. \(\tan^{-1}(2+\sqrt{3}-\sqrt{6}-\sqrt{2})\)
    Answer
    1. \(1.37\)
    2. \(−0.85\)
    3. \(1.23\)
    4. \(1.57\)
    5. \(−1.11\)
    6. undefined
    7. \(47.16^{\circ}\)
    8. \(-45^{\circ}\)
    9. \(75^{\circ}\)
    10. \(90.00^{\circ}\)
    11. \(67.5^{\circ}\)
    12. \(-7.5^{\circ}\)

    This page titled 19.2: Exercises was last modified on Mon, 02 May 2022 15:49:54 GMT and is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform.