What is the value of tan((3pi)/(10)) ?

The value of tan((3pi)/(10)) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)

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tan((3pi)/(10))

tan (\frac{3 π}{10})

\frac{( 3 10 + 5 2 ) 5 - 5}{20}

Solution steps

tan (\frac{3 π}{10})

Rewrite using trig identities:

\frac{sin ( \frac{3 π}{10} )}{cos ( \frac{3 π}{10} )}

= \frac{sin ( \frac{3 π}{10} )}{cos ( \frac{3 π}{10} )}

Rewrite using trig identities:

sin (\frac{3 π}{10}) = \frac{5 + 1}{4}

Rewrite using trig identities:

cos (\frac{3 π}{10}) = \frac{2 5 - 5}{4}

= \frac{\frac{5 + 1}{4}}{\frac{2 5 - 5}{4}}

Simplify

\frac{\frac{5 + 1}{4}}{\frac{2 5 - 5}{4}} : \frac{( 3 10 + 5 2 ) 5 - 5}{20}

= \frac{( 3 10 + 5 2 ) 5 - 5}{20}

6 sin (5 3^{\circ})

tan (111 0^{\circ})

arctan (\frac{50}{60})

3 sin (22 5^{\circ})

\frac{5.07}{sin ( 6 5 ^{\circ} )}

What is the value of tan((3pi)/(10)) ?
The value of tan((3pi)/(10)) is ((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)