Part - 2 Lecture - 2 Chapter 2 Inverse Trigonometric Functions
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Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.
Summary of this lecture:
Revision of Ranges of Inverse Trigonometric Functions
20 Practice Questions from my booklet
Evaluate each of the following:
1. \(\sin ^{-1} \left(-\frac{\sqrt{3} }{2} \right)\)
2. \(\cot ^{-1} \left(\frac{-1}{\sqrt{3} } \right)\) (NCERT Example 2)
3. \(\tan ^{-1} \left(-\frac{1}{\sqrt{3} } \right)\)
4. \(\tan ^{-1}(1)+\cos ^{-1} \left(-\frac{1}{2} \right)+\sin ^{-1} \left(-\frac{1}{2} \right)\)
5. \(\cos ^{-1} \left(\frac{1}{2} \right)+2\sin ^{-1} \left(\frac{1}{2} \right)\) (NCERT Exercise 2.2 Q12)
6. \(\tan ^{-1} \sqrt{3} -\sec ^{-1} (-2)\) (NCERT Exercise 2.2 Q14)
7. \(\sin ^{-1} \left(\sin \frac{4\pi }{5} \right)\)
8. \(\sin ^{-1} \left(\sin \frac{2\pi }{3} \right)\) (NCERT Exercise 2.2 Q16)
9. \(\tan ^{-1} \left(\tan \frac{3\pi }{4} \right)\) (NCERT Exercise 2.2 Q17)
10. \(\cos ^{-1} \left(\cos \frac{7\pi }{6} \right)\) (NCERT Exercise 2.2 Q19)
11. \(\sin \left(\frac{\pi }{3} -\sin ^{-1} \left(-\frac{1}{2} \right)\right)\) (NCERT Exercise 2.2 Q20)
12. \(\tan ^{-1} \sqrt{3} -\cot ^{-1} (-\sqrt{3} )\) (NCERT Exercise 2.2 Q21)
13. \(\csc ^{-1} (-2)\)
14. \(\sin ^{-1} \left(\sin \frac{3\pi }{5} \right)\) (NCERT Example 9)
16. \(\cos ^{-1} \left(\cos \frac{13\pi }{6} \right)\) (NCERT Miscellaneous Exercise Q1)
17. \(\tan ^{-1} \left(\tan \frac{7\pi }{6} \right)\) (NCERT Miscellaneous Exercise Q2)
18. \(\cos ^{-1} [\cos (-680{}^\circ )]\)
20. \(\tan ^{-1} \left(\tan \frac{5\pi }{6} \right)\)
