What is the value of arcsech(6/7) ?

The value of arcsech(6/7) is ln((7+sqrt(13))/6)

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arcsech(6/7)

arcsech (\frac{6}{7})

ln (\frac{7 + 13}{6})

Decimal Notation

0.56961 \dots

Solution steps

arcsech (\frac{6}{7})

Use the Hyperbolic identity:

arcsech (x) = ln (\frac{1}{x} + \frac{1}{x ^{2}} - 1)

= ln (\frac{1}{\frac{6}{7}} + \frac{1}{( \frac{6}{7} ) ^{2}} - 1)

ln (\frac{1}{\frac{6}{7}} + \frac{1}{( \frac{6}{7} ) ^{2}} - 1) = ln (\frac{7 + 13}{6})

ln (\frac{1}{\frac{6}{7}} + \frac{1}{( \frac{6}{7} ) ^{2}} - 1)

\frac{1}{\frac{6}{7}} = \frac{7}{6}

\frac{1}{\frac{6}{7}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{7}{6}

\frac{1}{( \frac{6}{7} ) ^{2}} - 1 = \frac{13}{6}

\frac{1}{( \frac{6}{7} ) ^{2}} - 1

\frac{1}{( \frac{6}{7} ) ^{2}} = \frac{49}{36}

\frac{1}{( \frac{6}{7} ) ^{2}}

(\frac{6}{7})^{2} = \frac{6 ^{2}}{7 ^{2}}

(\frac{6}{7})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{6 ^{2}}{7 ^{2}}

= \frac{1}{\frac{6 ^{2}}{7 ^{2}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{7 ^{2}}{6 ^{2}}

7^{2} = 49

= \frac{49}{6 ^{2}}

6^{2} = 36

= \frac{49}{36}

= \frac{49}{36} - 1

Join

\frac{49}{36} - 1 : \frac{13}{36}

\frac{49}{36} - 1

Convert element to fraction:

1 = \frac{1 \cdot 36}{36}

= \frac{49}{36} - \frac{1 \cdot 36}{36}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{49 - 1 \cdot 36}{36}

49 - 1 \cdot 36 = 13

49 - 1 \cdot 36

Multiply the numbers:

1 \cdot 36 = 36

= 49 - 36

Subtract the numbers:

49 - 36 = 13

= 13

= \frac{13}{36}

= \frac{13}{36}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{13}{36}

36 = 6

36

Factor the number:

36 = 6^{2}

= 6^{2}

Apply radical rule:

6^{2} = 6

= 6

= \frac{13}{6}

= ln (\frac{7}{6} + \frac{13}{6})

Join

\frac{7}{6} + \frac{13}{6} : \frac{7 + 13}{6}

\frac{7}{6} + \frac{13}{6}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{7 + 13}{6}

= ln (\frac{7 + 13}{6})

= ln (\frac{7 + 13}{6})

7 cos (2) (- \frac{π}{4})

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What is the value of arcsech(6/7) ?
The value of arcsech(6/7) is ln((7+sqrt(13))/6)