## Trigonometry (11th Edition) Clone

$\cot(-84^\circ03')$ is the answer in this exercise.
$$\tan174^\circ03'$$ Cotangent and tangent are cofunctions. So to write $\tan174^\circ03'$ in terms of cofunction, cotangent would be included. Now the job is to figure out the value of $\theta$, which must satisfy $$\cot\theta=\tan174^\circ03'\hspace{1cm}(1)$$ According to Cofunction Identity: $\cot\theta=\tan(90^\circ-\theta)$ Apply this to the equation $(1)$: $$\tan(90^\circ-\theta)=\tan174^\circ03'$$ $$90^\circ-\theta=174^\circ03'$$ $$\theta=90^\circ-174^\circ03'=-84^\circ03'$$ $\cot(-84^\circ03')$ is overall the answer to this exercise.