Page 20 - DMTH201_Basic Mathematics-1

Unit 1: Trigonometric Functions-I

1.5 Summary Notes

Inverse of a trigonometric function exists if we restrict the domain of it.
–1
(i) sin x = y if sin y = x where –1 x 1,

(ii) cos x = y if cos y = x where –1 x 1, 0 y
–1
(iii) tan x = y if tan y = x where x R,
–1
–1
(iv) cot x = y if cot y = x where x R, 0 < y <
–1
(v) sec x = y if sec y = x where x 1,

–1
(vi) cosec x = y if cosec y = x where x 1,0 < y

or

Graphs of inverse trigonometric functions can be represented in the given intervals by
interchanging the axes as in case of y = sin x, etc.

1.6 Self Assessment

Multiple Choice Questions
1. The Principal value of

(a) (b) (c) (d)

2. equals to
(a) (b) (c) (d)

3. is equal to

(a) (b) (c) (d)
–1
4. If sin x = y then
(a) o y p (b) (c) o < y < p (d)

5. is equal to
(a) (b) (c) (d)

6. is equal to

(a) (b) (c) o (d)
Fill in the blanks:
7. Inverse trigonometric function is also called as ………………
8. The value of an inverse trigonometric functions which lies in its principal value branch is
called as ……………… of that inverse trigonometric functions.

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