What is the value of tan((7pi)/5) ?

The value of tan((7pi)/5) is sqrt(5+2\sqrt{5)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan((7pi)/5)

tan (\frac{7 π}{5})

5 + 25

Solution steps

tan (\frac{7 π}{5})

tan (\frac{7 π}{5}) = tan (\frac{2 π}{5})

= tan (\frac{2 π}{5})

Rewrite using trig identities:

\frac{sin ( \frac{2 π}{5} )}{cos ( \frac{2 π}{5} )}

= \frac{sin ( \frac{2 π}{5} )}{cos ( \frac{2 π}{5} )}

Rewrite using trig identities:

sin (\frac{2 π}{5}) = \frac{2 5 + 5}{4}

Rewrite using trig identities:

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

= \frac{\frac{2 5 + 5}{4}}{\frac{2 3 - 5}{4}}

Simplify

\frac{\frac{2 5 + 5}{4}}{\frac{2 3 - 5}{4}} : 5 + 25

= 5 + 25

5 sin (9 0^{\circ})

cos^{3} (- \frac{3}{2}) + (- \frac{3}{2})^{4} - 3

cos (cos (0))

\frac{8}{sin ( 6 2 ^{\circ} )}

2 cos (\frac{4 π}{6})

What is the value of tan((7pi)/5) ?
The value of tan((7pi)/5) is sqrt(5+2\sqrt{5)}