# Exercise 2.1 Inverse Trigonometric Functions

## Topics/Questions discussed in this video:

00:00:30 What is the meaning of Inverse Trigonometry

00:03:40 Conditions when inverse of a function exists

00:17:50 Range of Inverse trigonometric functions (Principal values)

00:21:13 Derivation for negative input in inverse trigonometry

Find the principal values of the following:

00:29:13 NCERT Solutions Exercise 2.1 Question 1
\sin ^{-1} \left ( - \frac{1}{2} \right )

00:31:13 NCERT Solutions Exercise 2.1 Question 2
\cos ^{-1} \left ( \frac{\sqrt{3}}{2} \right )

00:32:23 NCERT Solutions Exercise 2.1 Question 3
\cosec ^{-1} \left ( 2 \right )

00:33:23 NCERT Solutions Exercise 2.1 Question 4
\tan ^{-1} \left ( \sqrt{3} \right )

00:34:15 NCERT Solutions Exercise 2.1 Question 5
\cos ^{-1} \left ( - \frac{1}{2} \right )

00:35:23 NCERT Solutions Exercise 2.1 Question 6
\tan ^{-1} \left ( - 1 \right )

00:36:13 NCERT Solutions Exercise 2.1 Question 7
\sec ^{-1} \left ( \frac{2}{\sqrt{3}} \right )

00:37:00 NCERT Solutions Exercise 2.1 Question 8
\cot ^{-1} \left ( \sqrt{3} \right )

00:37:33 NCERT Solutions Exercise 2.1 Question 9
\cos ^{-1} \left ( - \frac{1}{\sqrt{2}} \right )

00:38:43 NCERT Solutions Exercise 2.1 Question 10
\cosec ^{-1} \left ( - \sqrt{2} \right )

Find the values of the following:

00:39:23 NCERT Solutions Exercise 2.1 Question 11
\tan ^{-1} \left ( 1 \right )+\cos ^{-1} \left ( - \frac{1}{2} \right )+\sin ^{-1} \left ( - \frac{1}{2} \right )

00:41:13 NCERT Solutions Exercise 2.1 Question 12
\cos ^{-1} \left ( \frac{1}{2} \right )+2\sin ^{-1} \left ( - \frac{1}{2} \right )

00:42:03 NCERT Solutions Exercise 2.1 Question 13
If \sin ^ {-1}x = y

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