What is the value of cosh(pi/2) ?

The value of cosh(pi/2) is (e^pi+1)/(2e^{pi/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cosh(pi/2)

cosh (\frac{π}{2})

\frac{e ^{π} + 1}{2 e ^{\frac{π}{2}}}

Decimal Notation

2.50917 \dots

Solution steps

cosh (\frac{π}{2})

Use the Hyperbolic identity:

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

= \frac{e ^{\frac{π}{2}} + e ^{- \frac{π}{2}}}{2}

\frac{e ^{\frac{π}{2}} + e ^{- \frac{π}{2}}}{2} = \frac{e ^{π} + 1}{2 e ^{\frac{π}{2}}}

\frac{e ^{\frac{π}{2}} + e ^{- \frac{π}{2}}}{2}

Apply exponent rule:

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

= \frac{e ^{\frac{π}{2}} + \frac{1}{e ^{\frac{π}{2}}}}{2}

Join

e^{\frac{π}{2}} + \frac{1}{e ^{\frac{π}{2}}} : \frac{e ^{π} + 1}{e ^{\frac{π}{2}}}

e^{\frac{π}{2}} + \frac{1}{e ^{\frac{π}{2}}}

Convert element to fraction:

e^{\frac{π}{2}} = \frac{e ^{\frac{π}{2}} e ^{\frac{π}{2}}}{e ^{\frac{π}{2}}}

= \frac{e ^{\frac{π}{2}} e ^{\frac{π}{2}}}{e ^{\frac{π}{2}}} + \frac{1}{e ^{\frac{π}{2}}}

Since the denominators are equal, combine the fractions:

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

= \frac{e ^{\frac{π}{2}} e ^{\frac{π}{2}} + 1}{e ^{\frac{π}{2}}}

e^{\frac{π}{2}} e^{\frac{π}{2}} + 1 = e^{2 \cdot \frac{π}{2}} + 1

e^{\frac{π}{2}} e^{\frac{π}{2}} + 1

e^{\frac{π}{2}} e^{\frac{π}{2}} = e^{2 \cdot \frac{π}{2}}

e^{\frac{π}{2}} e^{\frac{π}{2}}

Apply exponent rule:

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

e^{\frac{π}{2}} e^{\frac{π}{2}} = e^{\frac{π}{2} + \frac{π}{2}}

= e^{\frac{π}{2} + \frac{π}{2}}

Add similar elements:

\frac{π}{2} + \frac{π}{2} = 2 \cdot \frac{π}{2}

= e^{2 \cdot \frac{π}{2}}

= e^{2 \cdot \frac{π}{2}} + 1

= \frac{e ^{2 \cdot \frac{π}{2}} + 1}{e ^{\frac{π}{2}}}

Multiply

2 \cdot \frac{π}{2} : π

2 \cdot \frac{π}{2}

Multiply fractions:

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

= \frac{π 2}{2}

Cancel the common factor:

2

= π

= \frac{e ^{π} + 1}{e ^{\frac{π}{2}}}

= \frac{\frac{e ^{π} + 1}{e ^{\frac{π}{2}}}}{2}

Apply the fraction rule:

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

= \frac{e ^{π} + 1}{e ^{\frac{π}{2}} \cdot 2}

= \frac{e ^{π} + 1}{2 e ^{\frac{π}{2}}}

cos (\frac{π}{3} + \frac{π}{4})

arctan (tan (\frac{π}{3}))

tan (arcsin (- \frac{3}{2}))

arctan (tan (\frac{π}{6}))

- 2 sec^{2} (0)

What is the value of cosh(pi/2) ?
The value of cosh(pi/2) is (e^pi+1)/(2e^{pi/2)}