Advertisements
Advertisements
Question
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
Options
`- (2pi)/3`
`-pi/3`
`(4pi)/3`
`(5pi)/3`
Advertisements
Solution
The principal value of `sin^-1 ((-sqrt(3))/2)` is `-pi/3`.
Explanation:
`sin^-1 ((-sqrt(3))/2) = sin^-1 (- sin pi/3)`
= `- sin^-1 (sin pi/3)`
= `- pi/3`.
APPEARS IN
RELATED QUESTIONS
The principal solution of the equation cot x=`-sqrt 3 ` is
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
Find the principal value of the following:
`tan^-1(cos pi/2)`
For the principal value, evaluate of the following:
`tan^-1(-1)+cos^-1(-1/sqrt2)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
cosec-1(-2)
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
Find the value of `sin[2cot^-1 ((-5)/12)]`
Find the value of `sin(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
The principal value branch of sec–1 is ______.
The value of `sin^-1 (cos((43pi)/5))` is ______.
If sin–1x + sin–1y = `pi/2`, then value of cos–1x + cos–1y is ______.
Find the value of `tan^-1 (tan (2pi)/3)`
Which of the following is the principal value branch of cosec–1x?
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
Assertion (A): Maximum value of (cos–1 x)2 is π2.
Reason (R): Range of the principal value branch of cos–1 x is `[(-π)/2, π/2]`.
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.
