What is the value of arcsinh(sqrt(3)) ?

The value of arcsinh(sqrt(3)) is ln(sqrt(3)+2)

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arcsinh(sqrt(3))

arcsinh (3)

ln (3 + 2)

Decimal Notation

1.31695 \dots

Solution steps

arcsinh (3)

Use the Hyperbolic identity:

arcsinh (x) = ln (x + x^{2} + 1)

= ln (3 + (3)^{2} + 1)

ln (3 + (3)^{2} + 1) = ln (3 + 2)

ln (3 + (3)^{2} + 1)

(3)^{2} + 1 = 2

(3)^{2} + 1

(3)^{2} = 3

(3)^{2}

Apply radical rule:

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

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

Apply exponent rule:

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

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

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 3

= 3 + 1

Add the numbers:

3 + 1 = 4

= 4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= ln (3 + 2)

= ln (3 + 2)

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

sin (10 5^{\circ}) sin (7 5^{\circ})

250 sec^{2} (\frac{π}{3})

arccos (0.342)

tan (\frac{8}{7})

What is the value of arcsinh(sqrt(3)) ?
The value of arcsinh(sqrt(3)) is ln(sqrt(3)+2)