Find the exact value of the expression.

Question

sec[sin^-1(-4/9)]?

Answer 1

Given that to find the value of

Let us considrer 4/9 as t

Substitute the value of t

=1.116

Answer 2

sec(sin^{- 1}(- 4/9)).

Reciprocal identity : sec x = 1/cos x.

= 1/[ cos(sin^{- 1} (- 4/9)) ]

Apply formula : cos(sin^{- 1} (x)) = √(1 - x²).

⇒ cos(sin^{- 1} (- 4/9))

= √(1 - (- 4/9)²)

= √(1 - (16/81))

= √((81 - 16)/81)

= √65/9.

1/[ cos(sin^{- 1} (- 4/9)) ] = 1/(√65/9) = 9/√65.

Therefore, sec(sin^{- 1} (- 4/9)) = 9/√65.