8.3E: Kazi za Trigonometric Inverse (Mazoezi)
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Kwa mazoezi yafuatayo, pata thamani halisi bila msaada wa calculator.
28. \(\sin ^{-1}(1)\)
29. \(\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)\)
30. \(\tan ^{-1}(-1)\)
31. \(\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)\)
32. \(\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)\)
33. \(\sin ^{-1}\left(\cos \left(\frac{\pi}{6}\right)\right)\)
34. \(\cos ^{-1}\left(\tan \left(\frac{3 \pi}{4}\right)\right)\)
35. \(\sin \left(\sec ^{-1}\left(\frac{3}{5}\right)\right)\)
36. \(\cot \left(\sin ^{-1}\left(\frac{3}{5}\right)\right)\)
37. \(\tan \left(\cos ^{-1}\left(\frac{5}{13}\right)\right)\)
38. \(\sin \left(\cos ^{-1}\left(\frac{x}{x+1}\right)\right)\)
39. Grafu\(f(x)=\cos x\) na\(f(x)=\sec x\) kwa muda\([0,2 \pi)\) na kuelezea uchunguzi wowote.
40. Grafu\(f(x)=\sin x\)\(f(x)=\csc x\) na kueleza uchunguzi wowote.
41. Graph kazi\(f(x)=\frac{x}{1}-\frac{x^{3}}{3 !}+\frac{x^{5}}{5 !}-\frac{x^{7}}{7 !}\) juu ya muda [-1,1] na kulinganisha grafu kwa grafu ya\(f(x)=\sin x\) juu ya muda huo. Eleza uchunguzi wowote.