Advertisements
Advertisements
Question
Find the principal value of the following: sin-1 `(1/sqrt(2))`
Advertisements
Solution
The principal value branch of sin-1x is `[- pi/2, pi/2]`.
Let sin-1`(1/sqrt(2)) = α, "where" (-pi)/(2) ≤ α ≤ pi/(2)`
∴ sin α = `(1)/(sqrt2) = sin pi/(4)`
∴ α = `pi/(4) ...[∵ - pi/2 ≤ pi/4 ≤ pi/2 ]`
∴ the principal value of sin-1`(1/sqrt(2)) "is" pi/(4)`.
APPEARS IN
RELATED QUESTIONS
Find the principal value of the following:
`tan^(-1) (-sqrt3)`
Find the principal value of the following:
`cot^(-1) (sqrt3)`
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
Find the domain of the following function:
`f(x)sin^-1sqrt(x^2-1)`
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
Find the domain of `f(x)=cotx+cot^-1x`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA.
Find the principal value of the following: tan- 1( - √3)
Find the principal value of the following: cos- 1`(-1/2)`
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`
Find the principal value of `sin^-1 1/sqrt(2)`
If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______
If 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ______.
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
`"sin"^-1 (-1/2)`
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
`"cos"^-1 ["cos" (2 "cot"^-1 (sqrt2 - 1))] =` ____________.
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
`"tan"(pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
The equation 2cos-1 x + sin-1 x `= (11pi)/6` has ____________.
If tan-1 x – tan-1 y = tan-1 A, then A is equal to ____________.
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
`"cos"^-1 ("cos" ((7pi)/6))` is equal to ____________.
`"tan"^-1 sqrt3 - "sec"^-1 (-2)` is equal to ____________.
If |Z1| = |Z2| and arg (Z1) + arg (Z2) = 0, then
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
Domain and Rariges of cos–1 is:-
What will be the principal value of `sin^-1(-1/2)`?
`sin(tan^-1x), |x| < 1` is equal to
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
If `sin(sin^-1 1/5 + cos^-1 x) = 1`, the what will be the value of x?
Find the principal value of `cot^-1 ((-1)/sqrt(3))`
`lim_(n→∞)tan{sum_(r = 1)^n tan^-1(1/(1 + r + r^2))}` is equal to ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
If tan 4θ = `tan(2/θ)`, then the general value of θ is ______.
