What is the value of tan^2((5pi)/4) ?

The value of tan^2((5pi)/4) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

tan^2((5pi)/4)

tan^{2} (\frac{5 π}{4})

1

Solution steps

tan^{2} (\frac{5 π}{4})

Rewrite using trig identities:

tan (\frac{5 π}{4}) = 1

tan (\frac{5 π}{4})

tan (\frac{5 π}{4}) = tan (\frac{π}{4})

tan (\frac{5 π}{4})

Rewrite

\frac{5 π}{4}

π + \frac{π}{4}

= tan (π + \frac{π}{4})

Apply the periodicity of

tan

tan (x + π) = tan (x)

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

= tan (\frac{π}{4})

= tan (\frac{π}{4})

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

= 1

= 1^{2}

Simplify

= 1