What is the value of sinh^3(3.002203156) ?

The value of sinh^3(3.002203156) is ((e^{6.00440…}-1)^3)/(8e^{9.00660…)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sinh^3(3.002203156)

sinh^{3} (3.002203156)

\frac{( e ^{6.00440 \dots} - 1 ) ^{3}}{8 e ^{9.00660 \dots}}

Decimal Notation

1012.07222 \dots

Solution steps

sinh^{3} (3.00220 \dots)

Rewrite using trig identities:

sinh (3.00220 \dots) = \frac{e ^{6.00440 \dots} - 1}{2 e ^{3.00220 \dots}}

sinh (3.00220 \dots)

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

= \frac{e ^{3.00220 \dots} - e ^{- 3.00220 \dots}}{2}

\frac{e ^{3.00220 \dots} - e ^{- 3.00220 \dots}}{2} = \frac{e ^{6.00440 \dots} - 1}{2 e ^{3.00220 \dots}}

\frac{e ^{3.00220 \dots} - e ^{- 3.00220 \dots}}{2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{e ^{3.00220 \dots} - \frac{1}{e ^{3.00220 \dots}}}{2}

Join

e^{3.00220 \dots} - \frac{1}{e ^{3.00220 \dots}} : \frac{e ^{6.00440 \dots} - 1}{e ^{3.00220 \dots}}

e^{3.00220 \dots} - \frac{1}{e ^{3.00220 \dots}}

Convert element to fraction:

e^{3.00220 \dots} = \frac{e ^{3.00220 \dots} e ^{3.00220 \dots}}{e ^{3.00220 \dots}}

= \frac{e ^{3.00220 \dots} e ^{3.00220 \dots}}{e ^{3.00220 \dots}} - \frac{1}{e ^{3.00220 \dots}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{3.00220 \dots} e ^{3.00220 \dots} - 1}{e ^{3.00220 \dots}}

e^{3.00220 \dots} e^{3.00220 \dots} - 1 = e^{6.00440 \dots} - 1

e^{3.00220 \dots} e^{3.00220 \dots} - 1

e^{3.00220 \dots} e^{3.00220 \dots} = e^{6.00440 \dots}

e^{3.00220 \dots} e^{3.00220 \dots}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{3.00220 \dots} e^{3.00220 \dots} = e^{3.00220 \dots + 3.00220 \dots}

= e^{3.00220 \dots + 3.00220 \dots}

Add the numbers:

3.00220 \dots + 3.00220 \dots = 6.00440 \dots

= e^{6.00440 \dots}

= e^{6.00440 \dots} - 1

= \frac{e ^{6.00440 \dots} - 1}{e ^{3.00220 \dots}}

= \frac{\frac{e ^{6.00440 \dots} - 1}{e ^{3.00220 \dots}}}{2}

Apply the fraction rule:

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

= \frac{e ^{6.00440 \dots} - 1}{e ^{3.00220 \dots} \cdot 2}

= \frac{e ^{6.00440 \dots} - 1}{2 e ^{3.00220 \dots}}

= (\frac{e ^{6.00440 \dots} - 1}{2 e ^{3.00220 \dots}})^{3}

(\frac{e ^{6.00440 \dots} - 1}{2 e ^{3.00220 \dots}})^{3} = \frac{( e ^{6.00440 \dots} - 1 ) ^{3}}{8 e ^{9.00660 \dots}}

(\frac{e ^{6.00440 \dots} - 1}{2 e ^{3.00220 \dots}})^{3}

Apply exponent rule:

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

= \frac{( e ^{6.00440 \dots} - 1 ) ^{3}}{( 2 e ^{3.00220 \dots} ) ^{3}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 e^{3.00220 \dots})^{3} = 2^{3} (e^{3.00220 \dots})^{3}

= \frac{( e ^{6.00440 \dots} - 1 ) ^{3}}{2 ^{3} ( e ^{3.00220 \dots} ) ^{3}}

(e^{3.00220 \dots})^{3} : e^{9.00660 \dots}

Apply exponent rule:

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

= e^{3.00220 \dots \cdot 3}

Multiply the numbers:

3.00220 \dots \cdot 3 = 9.00660 \dots

= e^{9.00660 \dots}

= \frac{( e ^{6.00440 \dots} - 1 ) ^{3}}{2 ^{3} e ^{9.00660 \dots}}

2^{3} = 8

= \frac{( e ^{6.00440 \dots} - 1 ) ^{3}}{8 e ^{9.00660 \dots}}

= \frac{( e ^{6.00440 \dots} - 1 ) ^{3}}{8 e ^{9.00660 \dots}}

cos (\frac{9}{4} π)

10 sin (1 5^{\circ})

1 - 2 sin^{2} (\frac{π}{4})

sin (45. 5^{\circ})

sin (1000 0^{\circ})

What is the value of sinh^3(3.002203156) ?
The value of sinh^3(3.002203156) is ((e^{6.00440…}-1)^3)/(8e^{9.00660…)}