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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. $\tan ^{-1} \left(\tan \frac{5\pi }{6} \right)$