What is the value of csc(arccos(-5/8)) ?

The value of csc(arccos(-5/8)) is (8sqrt(39))/(39)

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csc(arccos(-5/8))

csc (arccos (- \frac{5}{8}))

\frac{8 39}{39}

Decimal Notation

1.28102 \dots

Solution steps

csc (arccos (- \frac{5}{8}))

Rewrite using trig identities:

csc (arccos (- \frac{5}{8})) = \frac{1}{1 - ( - \frac{5}{8} ) ^{2}}

Use the following identity:

csc (arccos (x)) = \frac{1}{1 - x ^{2}}

= \frac{1}{1 - ( - \frac{5}{8} ) ^{2}}

= \frac{1}{1 - ( - \frac{5}{8} ) ^{2}}

Simplify

= \frac{8 39}{39}

\frac{( cos ( 4 5 ^{\circ} ) ) ^{2} + 3 csc ( 3 7 ^{\circ} )}{2 tan ( 4 5 ^{\circ} )}

cos^{2} (21 0^{\circ})

sin (\frac{π}{4}) sin (\frac{π}{12})

cos (12 3^{\circ})

cos (arccos (- 0.1))

What is the value of csc(arccos(-5/8)) ?
The value of csc(arccos(-5/8)) is (8sqrt(39))/(39)