What is the value of arctan(tan((11pi)/9)) ?

The value of arctan(tan((11pi)/9)) is (2pi)/9

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arctan(tan((11pi)/9))

arctan (tan (\frac{11 π}{9}))

\frac{2 π}{9}

Decimal Notation

40

Solution steps

arctan (tan (\frac{11 π}{9}))

Use the inverse trig property:

\frac{2 π}{9}

arctan (tan (\frac{11 π}{9}))

For

- \frac{π}{2} < x < \frac{π}{2}, a rc t an (t an (x)) = x

Rewrite using trig identities:

tan (\frac{11 π}{9}) = tan (\frac{2 π}{9})

tan (\frac{11 π}{9})

tan (x + π \cdot k) = tan (x)

= tan (\frac{11 π}{9} - 1 π)

= tan (\frac{2 π}{9})

= arctan (tan (\frac{2 π}{9}))

- \frac{π}{2} < \frac{2 π}{9} < \frac{π}{2}

= \frac{2 π}{9}

= \frac{2 π}{9}

- 2 sin (\frac{3 π}{2})

sin (5)

- 4 cos (\frac{π}{3}) (1 + ln (7 sin (\frac{π}{3})))

\frac{tan ( 4 0 ^{\circ} ) + tan ( 2 0 ^{\circ} )}{1 - tan ( 4 0 ^{\circ} ) tan ( 2 0 ^{\circ} )}

4 \cdot tan (6 0^{\circ})

What is the value of arctan(tan((11pi)/9)) ?
The value of arctan(tan((11pi)/9)) is (2pi)/9