Home
Class 12
MATHS
Find the principal value of each of th...

Find the principal value of each of the following:
(i) `sin^(-1)(-(sqrt(3))/2)`
(ii) `sin^(-1)(cos(2pi)/3)`
(iii) `sin^(-1)((sqrt(3)-1)/(2sqrt(2)))`

Text Solution

AI Generated Solution

To find the principal values of the given inverse trigonometric functions, we will solve each part step by step. ### (i) Find `sin^(-1)(-(sqrt(3))/2)` 1. **Identify the angle whose sine is `-(sqrt(3))/2`:** The sine function is negative in the fourth quadrant. The reference angle for `sqrt(3)/2` is `pi/3`. Therefore, the angle in the fourth quadrant is `-pi/3`. 2. **Write the principal value:** ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

  • JEE MAINS PREVIOUS YEAR

    RD SHARMA|Exercise EXAMPLE|1 Videos

Similar Questions

Explore conceptually related problems

Find the principal value of each of the following : cos^(-1)(-(sqrt(3))/(2))( ii) cos^(-1)(-(1)/(sqrt(2)))

Find the principal value of each of the following: sin^(-1)((sqrt(3)+1)/(2sqrt(2)))( (ii) sin^(-1)((cos(3 pi))/(4))( iii) sin^(-1)((tan(5 pi))/(4))

Find the principal values of the following : sin^(-1) (-(sqrt(3))/2)

Find the principal values of the following : sin^(-1)(1/(sqrt (2)))

Find the principal value of each of the following :(i)(sin^(-1)1)/(2)-2(sin^(-1)1)/(sqrt(2))( ii) sin^(-1){cos(sin^(-1)(sqrt((3)/(2)))}^(sqrt(2))

Find the principal value of each of the following: i) sin^(-1)(1/sqrt(2)) ii) cos^(-1)(sqrt(3))/2 iii) tan^(-1)(sqrt(3)) iv) "cosec"^(-1)(2)

Find the principal values of the following: sin^(-1)(-1/2) and tan^(-1)(-sqrt(3))

Find the principal value of each of the following: i) cot^(-1)(-sqrt(3)) ii) sec^(-1)(-sqrt(2)) iii) "cosec"^(-1)(-1) .

Find the principal values of the following : (i) sin ^(-1) ((-sqrt(3))/(2)) (ii) cot^(-1)sqrt(-3) (iii) cos^(-1)(-(1)/(2)) (iv) cosec^(-1)(sqrt(2)) (v) tan^(-1) (vi) cosec^(-1)(-1)

Find the principal value of each of the following: i) sin^(-1)(1/2) ii) sin^(-1)(-sqrt(3)/2) iii) tan^(-1)(-1/sqrt(3)) iv) tan^(-1)(-1) v) "cosec"^(-1)(-2) vi) tan^(-1)(-sqrt(3))

Home
Profile