What is the value of arctan(tan((7pi)/6)) ?

The value of arctan(tan((7pi)/6)) is pi/6

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arctan(tan((7pi)/6))

arctan (tan (\frac{7 π}{6}))

\frac{π}{6}

Decimal Notation

30

Solution steps

arctan (tan (\frac{7 π}{6}))

Use the inverse trig property:

\frac{π}{6}

arctan (tan (\frac{7 π}{6}))

For

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

Rewrite using trig identities:

tan (\frac{7 π}{6}) = tan (\frac{π}{6})

tan (\frac{7 π}{6})

tan (x + π \cdot k) = tan (x)

= tan (\frac{7 π}{6} - 1 π)

= tan (\frac{π}{6})

= arctan (tan (\frac{π}{6}))

- \frac{π}{2} < \frac{π}{6} < \frac{π}{2}

= \frac{π}{6}

= \frac{π}{6}

4 cos (3 0^{\circ})

csc^{2} (\frac{π}{4})

sin (5 6^{\circ})

cot (- \frac{π}{4})

- 2 cos (0)

What is the value of arctan(tan((7pi)/6)) ?
The value of arctan(tan((7pi)/6)) is pi/6