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Mathematics LibreTexts

19.2: Exercises

  • Page ID
    49074
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    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 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; a detailed edit history is available upon request.