What is the value of sec(arcsin(-1/2)) ?

The value of sec(arcsin(-1/2)) is (2sqrt(3))/3

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sec(arcsin(-1/2))

sec (arcsin (- \frac{1}{2}))

\frac{2 3}{3}

Decimal Notation

1.15470 \dots

Solution steps

sec (arcsin (- \frac{1}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{2 3}{3}

tan (2 2^{\circ})

cos (arcsin (0))

- cos (π) + cos (0)

1 - sin (\frac{π}{2})

sec (- 6 0^{\circ})

What is the value of sec(arcsin(-1/2)) ?
The value of sec(arcsin(-1/2)) is (2sqrt(3))/3