What is the value of tanh(3.2^2-9) ?

The value of tanh(3.2^2-9) is (e^{62/25}-1)/(e^{62/25)+1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tanh(3.2^2-9)

Solution

tanh (3. 2^{2} - 9)

Solution

\frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{62}{25}} + 1}

Decimal Notation

0.84545 \dots

Solution steps

tanh (3. 2^{2} - 9)

= tanh ((\frac{16}{5})^{2} - 9)

Simplify:

(\frac{16}{5})^{2} - 9 = \frac{31}{25}

(\frac{16}{5})^{2} - 9

Apply exponent rule:

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

= \frac{1 6 ^{2}}{5 ^{2}} - 9

Convert element to fraction:

9 = \frac{9 \cdot 5 ^{2}}{5 ^{2}}

= \frac{1 6 ^{2}}{5 ^{2}} - \frac{9 \cdot 5 ^{2}}{5 ^{2}}

Since the denominators are equal, combine the fractions:

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

= \frac{1 6 ^{2} - 9 \cdot 5 ^{2}}{5 ^{2}}

1 6^{2} - 9 \cdot 5^{2} = 31

1 6^{2} - 9 \cdot 5^{2}

1 6^{2} = 256

1 6^{2}

1 6^{2} = 256

= 256

9 \cdot 5^{2} = 225

9 \cdot 5^{2}

5^{2} = 25

= 9 \cdot 25

Multiply the numbers:

9 \cdot 25 = 225

= 225

= 256 - 225

Subtract the numbers:

256 - 225 = 31

= 31

= \frac{31}{5 ^{2}}

5^{2} = 25

= \frac{31}{25}

= tanh (\frac{31}{25})

Rewrite using trig identities:

\frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{62}{25}} + 1}

tanh (\frac{31}{25})

Use the Hyperbolic identity:

tanh (x) = \frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}}

= \frac{e ^{\frac{31}{25}} - e ^{- \frac{31}{25}}}{e ^{\frac{31}{25}} + e ^{- \frac{31}{25}}}

\frac{e ^{\frac{31}{25}} - e ^{- \frac{31}{25}}}{e ^{\frac{31}{25}} + e ^{- \frac{31}{25}}} = \frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{62}{25}} + 1}

\frac{e ^{\frac{31}{25}} - e ^{- \frac{31}{25}}}{e ^{\frac{31}{25}} + e ^{- \frac{31}{25}}}

Apply exponent rule:

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

e^{- \frac{31}{25}} = \frac{1}{e ^{\frac{31}{25}}}

= \frac{e ^{\frac{31}{25}} - \frac{1}{e ^{\frac{31}{25}}}}{e ^{\frac{31}{25}} + \frac{1}{e ^{\frac{31}{25}}}}

Join

e^{\frac{31}{25}} + \frac{1}{e ^{\frac{31}{25}}} : \frac{e ^{\frac{62}{25}} + 1}{e ^{\frac{31}{25}}}

e^{\frac{31}{25}} + \frac{1}{e ^{\frac{31}{25}}}

Convert element to fraction:

e^{\frac{31}{25}} = \frac{e ^{\frac{31}{25}} e ^{\frac{31}{25}}}{e ^{\frac{31}{25}}}

= \frac{e ^{\frac{31}{25}} e ^{\frac{31}{25}}}{e ^{\frac{31}{25}}} + \frac{1}{e ^{\frac{31}{25}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{31}{25}} e ^{\frac{31}{25}} + 1}{e ^{\frac{31}{25}}}

e^{\frac{31}{25}} e^{\frac{31}{25}} + 1 = e^{2 \cdot \frac{31}{25}} + 1

e^{\frac{31}{25}} e^{\frac{31}{25}} + 1

e^{\frac{31}{25}} e^{\frac{31}{25}} = e^{2 \cdot \frac{31}{25}}

e^{\frac{31}{25}} e^{\frac{31}{25}}

Apply exponent rule:

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

e^{\frac{31}{25}} e^{\frac{31}{25}} = e^{\frac{31}{25} + \frac{31}{25}}

= e^{\frac{31}{25} + \frac{31}{25}}

Add similar elements:

\frac{31}{25} + \frac{31}{25} = 2 \cdot \frac{31}{25}

= e^{2 \cdot \frac{31}{25}}

= e^{2 \cdot \frac{31}{25}} + 1

= \frac{e ^{2 \cdot \frac{31}{25}} + 1}{e ^{\frac{31}{25}}}

Multiply

2 \cdot \frac{31}{25} : \frac{62}{25}

2 \cdot \frac{31}{25}

Multiply fractions:

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

= \frac{31 \cdot 2}{25}

Multiply the numbers:

31 \cdot 2 = 62

= \frac{62}{25}

= \frac{e ^{\frac{62}{25}} + 1}{e ^{\frac{31}{25}}}

= \frac{e ^{\frac{31}{25}} - \frac{1}{e ^{\frac{31}{25}}}}{\frac{e ^{\frac{62}{25}} + 1}{e ^{\frac{31}{25}}}}

Join

e^{\frac{31}{25}} - \frac{1}{e ^{\frac{31}{25}}} : \frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{31}{25}}}

e^{\frac{31}{25}} - \frac{1}{e ^{\frac{31}{25}}}

Convert element to fraction:

e^{\frac{31}{25}} = \frac{e ^{\frac{31}{25}} e ^{\frac{31}{25}}}{e ^{\frac{31}{25}}}

= \frac{e ^{\frac{31}{25}} e ^{\frac{31}{25}}}{e ^{\frac{31}{25}}} - \frac{1}{e ^{\frac{31}{25}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{31}{25}} e ^{\frac{31}{25}} - 1}{e ^{\frac{31}{25}}}

e^{\frac{31}{25}} e^{\frac{31}{25}} - 1 = e^{2 \cdot \frac{31}{25}} - 1

e^{\frac{31}{25}} e^{\frac{31}{25}} - 1

e^{\frac{31}{25}} e^{\frac{31}{25}} = e^{2 \cdot \frac{31}{25}}

e^{\frac{31}{25}} e^{\frac{31}{25}}

Apply exponent rule:

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

e^{\frac{31}{25}} e^{\frac{31}{25}} = e^{\frac{31}{25} + \frac{31}{25}}

= e^{\frac{31}{25} + \frac{31}{25}}

Add similar elements:

\frac{31}{25} + \frac{31}{25} = 2 \cdot \frac{31}{25}

= e^{2 \cdot \frac{31}{25}}

= e^{2 \cdot \frac{31}{25}} - 1

= \frac{e ^{2 \cdot \frac{31}{25}} - 1}{e ^{\frac{31}{25}}}

Multiply

2 \cdot \frac{31}{25} : \frac{62}{25}

2 \cdot \frac{31}{25}

Multiply fractions:

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

= \frac{31 \cdot 2}{25}

Multiply the numbers:

31 \cdot 2 = 62

= \frac{62}{25}

= \frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{31}{25}}}

= \frac{\frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{31}{25}}}}{\frac{e ^{\frac{62}{25}} + 1}{e ^{\frac{31}{25}}}}

Divide fractions:

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

= \frac{( e ^{\frac{62}{25}} - 1 ) e ^{\frac{31}{25}}}{e ^{\frac{31}{25}} ( e ^{\frac{62}{25}} + 1 )}

Cancel the common factor:

e^{\frac{31}{25}}

= \frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{62}{25}} + 1}

= \frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{62}{25}} + 1}

= \frac{e ^{\frac{62}{25}} - 1}{e ^{\frac{62}{25}} + 1}

Popular Examples

sec^2(pi/6)-tan^2(pi/6)-cos^2(pi/6)

sec^{2} (\frac{π}{6}) - tan^{2} (\frac{π}{6}) - cos^{2} (\frac{π}{6})

20*sin(40)

20 \cdot sin (4 0^{\circ})

4sin(4pi)

4 sin (4 π)

tan^2(61)

tan^{2} (6 1^{\circ})

1^2+ln(1)-sin(1)

1^{2} + ln (1) - sin (1)

Frequently Asked Questions (FAQ)

What is the value of tanh(3.2^2-9) ?
The value of tanh(3.2^2-9) is (e^{62/25}-1)/(e^{62/25)+1}