What is the value of sec(arcsin(-1/5)) ?

The value of sec(arcsin(-1/5)) is (5sqrt(6))/(12)

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sec(arcsin(-1/5))

sec (arcsin (- \frac{1}{5}))

\frac{5 6}{12}

Decimal Notation

1.02062 \dots

Solution steps

sec (arcsin (- \frac{1}{5}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{5 6}{12}

arctan (\frac{150}{200})

cos (2 π + \frac{π}{2})

arctan (\frac{2}{- 7})

\frac{sin ( \frac{2 3 ^{\circ} + 6 0 ^{\circ}}{2} )}{sin ( \frac{6 0 ^{\circ}}{2} )}

6 sin (2 (\frac{π}{3}))

What is the value of sec(arcsin(-1/5)) ?
The value of sec(arcsin(-1/5)) is (5sqrt(6))/(12)