What is the value of csc(arccos((sqrt(21))/7)) ?

The value of csc(arccos((sqrt(21))/7)) is (sqrt(7))/2

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csc(arccos((sqrt(21))/7))

csc (arccos (\frac{21}{7}))

\frac{7}{2}

Decimal Notation

1.32287 \dots

Solution steps

csc (arccos (\frac{21}{7}))

Rewrite using trig identities:

csc (arccos (\frac{21}{7})) = \frac{1}{1 - ( \frac{21}{7} ) ^{2}}

Use the following identity:

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

= \frac{1}{1 - ( \frac{21}{7} ) ^{2}}

= \frac{1}{1 - ( \frac{21}{7} ) ^{2}}

Simplify

= \frac{7}{2}

cos (2 \frac{3 π}{4})

- ln ∣ cos (0) ∣

tan (- \frac{7 π}{2})

1 + cos (\frac{3 π}{2})

12 sin (\frac{π}{3})

What is the value of csc(arccos((sqrt(21))/7)) ?
The value of csc(arccos((sqrt(21))/7)) is (sqrt(7))/2