The value of :sin-1(cos((33π /5)))

Question

The value of :sin-1(cos((33π /5))) (A) (3π :/5) (B) (-5π :/5) (C) (π :/10) (D) (-π :/10)

Tardigrade Admin · Accepted Answer

sin-1(cos((33π/5))) = sin-1(cos(6π+(3π /5))) = sin-1(cos(3π /5)) = sin-1 [cos((π/2)+(π /10))] = sin-1( -sin (π /10)) = -sin-1( sin (π /10)) = - (π /10)

Q. The value of $s i n^{- 1} (cos (\frac{33 π}{5}))$

$\frac{3 π}{5}$

$\frac{- 5 π}{5}$

$\frac{π}{10}$

$\frac{- π}{10}$

$s i n^{- 1} (cos (\frac{33 π}{5}))$
$= s i n^{- 1} (cos (6 π + \frac{3 π}{5}))$
$= s i n^{- 1} (cos \frac{3 π}{5})$
$= s i n^{- 1} [cos (\frac{π}{2} + \frac{π}{10})]$
$= s i n^{- 1} (- s in \frac{π}{10})$
$= - s i n^{- 1} (s in \frac{π}{10}) = - \frac{π}{10}$

Q. The value of sin−1(cos(533π​))

53π​

5−5π​

10π​

10−π​