Question

The value of `sin^-1 [cos((33pi)/5)]` is ______.

Options

• `(3pi)/5`

• `(-7pi)/5`

• `pi/10`

• `(-pi)/10`

Answer 1

The value of `sin^-1 [cos((33pi)/5)]` is `(-pi)/10`.

Explanation:

`sin^-1 [cos((33pi)/5)] = sin^-1[cos(6pi + (3pi)/5)]`

= `sin^-1[cos  (3pi)/5]` .......[∵ cos(2nπ + x) = cos x]

= `sin^-1 [cos(pi/2 + pi/10)]`

= `sin^-1[-sin (pi/10)]`  ......`[because cos(pi/2 + theta) = - sin theta]`

= `sin^-1[sin((-pi)/10)]`

= `(-pi)/10`