What is the value of sec(arcsin(-4/5)) ?

The value of sec(arcsin(-4/5)) is 5/3

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sec(arcsin(-4/5))

sec (arcsin (- \frac{4}{5}))

\frac{5}{3}

Decimal Notation

1.66666 \dots

Solution steps

sec (arcsin (- \frac{4}{5}))

Rewrite using trig identities:

sec (arcsin (- \frac{4}{5})) = \frac{1 - ( - \frac{4}{5} ) ^{2}}{1 - ( - \frac{4}{5} ) ^{2}}

Use the following identity:

sec (arcsin (x)) = \frac{1 - x ^{2}}{1 - x ^{2}}

= \frac{1 - ( - \frac{4}{5} ) ^{2}}{1 - ( - \frac{4}{5} ) ^{2}}

= \frac{1 - ( - \frac{4}{5} ) ^{2}}{1 - ( - \frac{4}{5} ) ^{2}}

Simplify

= \frac{5}{3}

- ln cos (\frac{π}{3})

24 \cdot cos (3 0^{\circ})

sin^{2} (8.75)

sin (3.2)

sin^{2} (2 2^{\circ})