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

The value of sec(arcsin(-(sqrt(2))/2)) is square root of 2

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sec(arcsin(-(sqrt(2))/2))

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

2

Decimal Notation

1.41421 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= 2

2 sin^{2} (x) - sin (x) - 3 = 0

sec (21 0^{\circ})

tan (x) + cot (x) = sec (x) csc (x)

sec (\frac{7 π}{6})

sec (\frac{π}{6})

What is the value of sec(arcsin(-(sqrt(2))/2)) ?
The value of sec(arcsin(-(sqrt(2))/2)) is square root of 2