Find the principal value cos-1 ((-√3/2))

Question

Find the principal value cos-1 ((-√3/2)) (A) (5π/6) (B) (π/6) (C) (4π/9) (D) (2π/3)

Tardigrade Admin · Accepted Answer

Let cos-1 ((-√3/2)) = θ ⇒ cos θ = (-√3/2) = -cos (π /6) = cos(π - (π/6)) = cos (5π/6) ⇒ θ = (5π /6)∈ [0, π] ∴ Principal value of cos-1 ((-√3/2)) is (5π/6)

Q. Find the principal value $co s^{- 1} (\frac{- 3}{2})$

$\frac{5 π}{6}$

$\frac{π}{6}$

$\frac{4 π}{9}$

$\frac{2 π}{3}$

Let $co s^{- 1} (\frac{- 3}{2}) = θ$
$\Rightarrow cos θ = \frac{- 3}{2}$
$= - cos \frac{π}{6}$
$= cos (π - \frac{π}{6})$
$= cos \frac{5 π}{6}$
$\Rightarrow θ = \frac{5 π}{6} \in [0, π]$
$∴$ Principal value of $co s^{- 1} (\frac{- 3}{2})$ is $\frac{5 π}{6}$

Q. Find the principal value cos−1(2−3​​)

65π​

6π​

94π​

32π​