inverse_trigonometric_lecture_2_part_2
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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)