What is the value of arctan(cot((3pi)/4)) ?

The value of arctan(cot((3pi)/4)) is -pi/4

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arctan(cot((3pi)/4))

arctan (cot (\frac{3 π}{4}))

- \frac{π}{4}

Decimal Notation

- 45

Solution steps

arctan (cot (\frac{3 π}{4}))

Rewrite using trig identities:

cot (\frac{3 π}{4}) = tan (- \frac{π}{4})

cot (\frac{3 π}{4})

tan (\frac{π}{2} - x) = cot (x)

= tan (\frac{π}{2} - \frac{3 π}{4})

= tan (- \frac{π}{4})

= arctan (tan (- \frac{π}{4}))

Use the inverse trig property:

- \frac{π}{4}

arctan (tan (- \frac{π}{4}))

For

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

- \frac{π}{2} < - \frac{π}{4} < \frac{π}{2}

= - \frac{π}{4}

= - \frac{π}{4}

arccos (\frac{6}{14})

- \frac{cos ^{3} ( π )}{3}

3 (sin (3 0^{\circ})) - cot (4 5^{\circ})

cos (arctan (- \frac{10}{3}))

sin (35. 5^{\circ})

What is the value of arctan(cot((3pi)/4)) ?
The value of arctan(cot((3pi)/4)) is -pi/4