What is the value of arctan(tan(9.8488500000000…)) ?

The value of arctan(tan(9.8488500000000…)) is (196977-60000pi)/(20000)

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arctan(tan(9.8488500000000…))

arctan (tan (9.8488500000000 \dots))

\frac{196977 - 60000 π}{20000}

Decimal Notation

24.3

Solution steps

arctan (tan (9.84885 \dots))

= arctan (tan (\frac{196977}{20000}))

Use the inverse trig property:

\frac{196977 - 60000 π}{20000}

arctan (tan (\frac{196977}{20000}))

For

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

Rewrite using trig identities:

tan (\frac{196977}{20000}) = tan (\frac{196977 - 60000 π}{20000})

tan (\frac{196977}{20000})

tan (x + π \cdot k) = tan (x)

= tan (\frac{196977}{20000} - 3 π)

= tan (\frac{196977 - 60000 π}{20000})

= arctan (tan (\frac{196977 - 60000 π}{20000}))

- \frac{π}{2} < \frac{196977 - 60000 π}{20000} < \frac{π}{2}

= \frac{196977 - 60000 π}{20000}

= \frac{196977 - 60000 π}{20000}

6 cos (3 π)

cos (- 3 6^{\circ})

arctan (\frac{4}{- 6})

arctan (\frac{12}{17})

cot (- 40 5^{\circ})

What is the value of arctan(tan(9.8488500000000…)) ?
The value of arctan(tan(9.8488500000000…)) is (196977-60000pi)/(20000)