19.2: Exercises
- Page ID
- 49074
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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.
- \(y=\sin^{-1}(x)\)
- \(y=\cos^{-1}(x)\)
- \( y=\tan^{-1}(x)\)
- Answer
-
\(\begin{aligned}&-2 \leq x \leq 2 \\&-2 \leq y \leq 2\end{aligned}\)
\(\begin{aligned}&-2 \leq x \leq 2 \\&-1 \leq y \leq 4\end{aligned} \)
\(\begin{aligned}-10 & \leq x \leq 10 \\-2 & \leq y \leq 2\end{aligned} \)
Find the exact value of the inverse trigonometric function.
- \(\tan^{-1}(\sqrt{3})\)
- \(\sin^{-1}\left(\dfrac{1}{2}\right)\)
- \(\cos^{-1}\left(\dfrac{1}{2}\right)\)
- \(\tan^{-1}(0)\)
- \(\cos^{-1}\left(\dfrac{\sqrt{2}}{2}\right)\)
- \(\cos^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)\)
- \(\sin^{-1}(-1)\)
- \(\tan^{-1}(-\sqrt{3})\)
- \(\cos^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\)
- \(\sin^{-1}\left(-\dfrac{\sqrt{2}}{2}\right)\)
- \(\sin^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\)
- \(\tan^{-1}\left(-\dfrac{1}{\sqrt{3}}\right)\)
- Answer
-
- \(\dfrac{\pi}{3}\)
- \(\dfrac{\pi}{6}\)
- \(\dfrac{\pi}{3}\)
- \(0\)
- \(\dfrac{\pi}{4}\)
- \(\dfrac{3\pi}{4}\)
- \(-\dfrac{\pi}{2}\)
- \(-\dfrac{\pi}{3}\)
- \(\dfrac{5 \pi}{6}\)
- \(-\dfrac{\pi}{4}\)
- \(-\dfrac{\pi}{3}\)
- \(-\dfrac{\pi}{6}\)
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.
- \(\cos^{-1}(0.2)\)
- \(\sin^{-1}(-0.75)\)
- \(\cos^{-1}\left(\dfrac{1}{3}\right)\)
- \(\tan^{-1}(100,000)\)
- \(\tan^{-1}(-2)\)
- \(\cos^{-1}(-2)\)
For parts (g)-(l), write your answer in degree mode.
- \(\cos^{-1}(0.68)\)
- \(\tan^{-1}(-1)\)
- \(\sin^{-1}\left(\dfrac{\sqrt{2}+\sqrt{6}}{4}\right)\)
- \(\tan^{-1}(100,000)\)
- \(\cos^{-1}\left(\dfrac{\sqrt{2-\sqrt{2}}}{2}\right)\)
- \(\tan^{-1}(2+\sqrt{3}-\sqrt{6}-\sqrt{2})\)
- Answer
-
- \(1.37\)
- \(−0.85\)
- \(1.23\)
- \(1.57\)
- \(−1.11\)
- undefined
- \(47.16^{\circ}\)
- \(-45^{\circ}\)
- \(75^{\circ}\)
- \(90.00^{\circ}\)
- \(67.5^{\circ}\)
- \(-7.5^{\circ}\)