What is the value of sec(arcsin(-1/4)) ?

The value of sec(arcsin(-1/4)) is (4sqrt(15))/(15)

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sec(arcsin(-1/4))

sec (arcsin (- \frac{1}{4}))

\frac{4 15}{15}

Decimal Notation

1.03279 \dots

Solution steps

sec (arcsin (- \frac{1}{4}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{4 15}{15}

arccos (\frac{2}{3})

arccot (\frac{5}{4})

cos (arccos (\frac{3}{5}))

arctan (\frac{7}{3})

- 2 sin (\frac{5 π}{3})

What is the value of sec(arcsin(-1/4)) ?
The value of sec(arcsin(-1/4)) is (4sqrt(15))/(15)