What is the value of arcsech(2/3) ?

The value of arcsech(2/3) is ln((3+sqrt(5))/2)

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arcsech(2/3)

arcsech (\frac{2}{3})

ln (\frac{3 + 5}{2})

Decimal Notation

0.96242 \dots

Solution steps

arcsech (\frac{2}{3})

Use the Hyperbolic identity:

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

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

ln (\frac{1}{\frac{2}{3}} + \frac{1}{( \frac{2}{3} ) ^{2}} - 1) = ln (\frac{3 + 5}{2})

ln (\frac{1}{\frac{2}{3}} + \frac{1}{( \frac{2}{3} ) ^{2}} - 1)

\frac{1}{\frac{2}{3}} = \frac{3}{2}

\frac{1}{\frac{2}{3}}

Apply the fraction rule:

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

= \frac{3}{2}

\frac{1}{( \frac{2}{3} ) ^{2}} - 1 = \frac{5}{2}

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

\frac{1}{( \frac{2}{3} ) ^{2}} = \frac{9}{4}

\frac{1}{( \frac{2}{3} ) ^{2}}

(\frac{2}{3})^{2} = \frac{2 ^{2}}{3 ^{2}}

(\frac{2}{3})^{2}

Apply exponent rule:

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

= \frac{2 ^{2}}{3 ^{2}}

= \frac{1}{\frac{2 ^{2}}{3 ^{2}}}

Apply the fraction rule:

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

= \frac{3 ^{2}}{2 ^{2}}

3^{2} = 9

= \frac{9}{2 ^{2}}

2^{2} = 4

= \frac{9}{4}

= \frac{9}{4} - 1

Join

\frac{9}{4} - 1 : \frac{5}{4}

\frac{9}{4} - 1

Convert element to fraction:

1 = \frac{1 \cdot 4}{4}

= \frac{9}{4} - \frac{1 \cdot 4}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{9 - 1 \cdot 4}{4}

9 - 1 \cdot 4 = 5

9 - 1 \cdot 4

Multiply the numbers:

1 \cdot 4 = 4

= 9 - 4

Subtract the numbers:

9 - 4 = 5

= 5

= \frac{5}{4}

= \frac{5}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{5}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{5}{2}

= ln (\frac{3}{2} + \frac{5}{2})

Join

\frac{3}{2} + \frac{5}{2} : \frac{3 + 5}{2}

\frac{3}{2} + \frac{5}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{3 + 5}{2}

= ln (\frac{3 + 5}{2})

= ln (\frac{3 + 5}{2})

sin (\frac{1}{\frac{2}{11 π}})

sec (- 1 4^{\circ})

60 \cdot sin (4 5^{\circ})

2 cos^{2} (\frac{3 π}{4}) - 1

sec (0.64)

What is the value of arcsech(2/3) ?
The value of arcsech(2/3) is ln((3+sqrt(5))/2)