What is the value of sec(arcsin(-3/4)) ?

The value of sec(arcsin(-3/4)) is (4sqrt(7))/7

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sec(arcsin(-3/4))

sec (arcsin (- \frac{3}{4}))

\frac{4 7}{7}

Decimal Notation

1.51185 \dots

Solution steps

sec (arcsin (- \frac{3}{4}))

Rewrite using trig identities:

sec (arcsin (- \frac{3}{4})) = \frac{1 - ( - \frac{3}{4} ) ^{2}}{1 - ( - \frac{3}{4} ) ^{2}}

Use the following identity:

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

= \frac{1 - ( - \frac{3}{4} ) ^{2}}{1 - ( - \frac{3}{4} ) ^{2}}

= \frac{1 - ( - \frac{3}{4} ) ^{2}}{1 - ( - \frac{3}{4} ) ^{2}}

Simplify

= \frac{4 7}{7}

arcsin (sin (- \frac{8 π}{5}))

sec (arctan (- 4))

\frac{cos ( 3 0 ^{\circ} ) + tan ( 6 0 ^{\circ} )}{2 - cos ^{2} ( 4 5 ^{\circ} )}

sin (\frac{arctan ( \frac{4}{3} )}{2})

cos (30 5^{\circ})

What is the value of sec(arcsin(-3/4)) ?
The value of sec(arcsin(-3/4)) is (4sqrt(7))/7