What is the value of sqrt(2/(pi*0.5)tan((pi*0.5)/2)) ?

The value of sqrt(2/(pi*0.5)tan((pi*0.5)/2)) is (2sqrt(pi))/pi

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Popular Trigonometry >

sqrt(2/(pi0.5)tan((pi0.5)/2))

Solution

\frac{2}{π \cdot 0.5} tan (\frac{π \cdot 0.5}{2})

Solution

\frac{2 π}{π}

Decimal

1.12837 \dots

Solution steps

\frac{2}{π 0.5} tan (\frac{π 0.5}{2})

= \frac{2}{π \frac{1}{2}} tan (\frac{π \frac{1}{2}}{2})

Simplify:

\frac{π \frac{1}{2}}{2} = \frac{π}{4}

\frac{π \frac{1}{2}}{2}

Multiply

π \frac{1}{2} : \frac{π}{2}

π \frac{1}{2}

Multiply fractions:

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

= \frac{1 π}{2}

Multiply:

1 π = π

= \frac{π}{2}

= \frac{\frac{π}{2}}{2}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

\frac{2}{π \frac{1}{2}} tan (\frac{π}{4}) = \frac{2 π tan ( \frac{π}{4} )}{π}

\frac{2}{π \frac{1}{2}} tan (\frac{π}{4})

Multiply

\frac{2}{π \frac{1}{2}} tan (\frac{π}{4}) : \frac{4 tan ( \frac{π}{4} )}{π}

\frac{2}{π \frac{1}{2}} tan (\frac{π}{4})

Multiply fractions:

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

= \frac{2 tan ( \frac{π}{4} )}{π \frac{1}{2}}

Multiply

π \frac{1}{2} : \frac{π}{2}

π \frac{1}{2}

Multiply fractions:

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

= \frac{1 π}{2}

Multiply:

1 π = π

= \frac{π}{2}

= \frac{2 tan ( \frac{π}{4} )}{\frac{π}{2}}

Apply the fraction rule:

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

= \frac{2 tan ( \frac{π}{4} ) \cdot 2}{π}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 tan ( \frac{π}{4} )}{π}

= \frac{4 tan ( \frac{π}{4} )}{π}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4 tan ( \frac{π}{4} )}{π}

Apply radical rule:

assuming

a \geq 0, b \geq 0

4 tan (\frac{π}{4}) = 4 tan (\frac{π}{4})

= \frac{4 tan ( \frac{π}{4} )}{π}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{2 tan ( \frac{π}{4} )}{π}

Rationalize

\frac{2 tan ( \frac{π}{4} )}{π} : \frac{2 π tan ( \frac{π}{4} )}{π}

\frac{2 tan ( \frac{π}{4} )}{π}

Multiply by the conjugate

\frac{π}{π}

= \frac{2 tan ( \frac{π}{4} ) π}{π π}

π π = π

π π

Apply radical rule:

a a = a

π π = π

= π

= \frac{2 π tan ( \frac{π}{4} )}{π}

= \frac{2 π tan ( \frac{π}{4} )}{π}

= \frac{2 π tan ( \frac{π}{4} )}{π}

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= \frac{2 π 1}{π}

Simplify

= \frac{2 π}{π}

Popular Examples

sqrt(3[cos((4pi)/9)+isin((4pi)/9)])

Frequently Asked Questions (FAQ)

What is the value of sqrt(2/(pi*0.5)tan((pi*0.5)/2)) ?
The value of sqrt(2/(pi*0.5)tan((pi*0.5)/2)) is (2sqrt(pi))/pi