Solve the equation for exact solutions.
-$\arctan x = \operatorname { arccot } \frac { 6 } { 19 }$
A) $\varnothing$
B) $\{ 0 \}$
C) $\left\{ \frac { 19 } { 6 } \right\}$
D) $\left\{ \frac { 6 } { 19 } \right\}$

Question

Quizplus · Accepted Answer

The arccotangent function, $\operatorname{arccot}$, is the inverse of the cotangent function. For $\operatorname{arccot} \frac{6}{19}$, this value is equivalent to the angle whose cotangent is $\frac{6}{19}$. Since $\cot \theta = \frac{1}{\tan \theta}$, we have $\tan(\operatorname{arccot} \frac{6}{19}) = \frac{19}{6}$. Therefore, $\arctan x = \frac{19}{6}$ implies $x = \frac{19}{6}$.

Solve the Equation for Exact Solutions arctan⁡x=arccot⁡619\arctan x = \operatorname { arccot } \frac { 6 } { 19 }arctanx=arccot196​

Solve the Equation for Exact Solutions $\arctan x = \operatorname { arccot } \frac { 6 } { 19 }$