Q.Convert $\dfrac{7\pi}{6}$ radians into degree measure.

To convert a radian measure into degrees, multiply by the reciprocal conversion factor $180/\pi$, since $\pi$ radians $=180^\circ$.

$\dfrac{7\pi}{6}\times\dfrac{180^\circ}{\pi} = \dfrac{7\times180}{6}^\circ = \dfrac{1260}{6}^\circ = 210^\circ$.

Step 1 — recall the conversion relation. $\pi$ radians $=180^\circ$, so $1$ radian $=\dfrac{180^\circ}{\pi}$.

Step 2 — apply it. $\dfrac{7\pi}{6}\times\dfrac{180}{\pi}$: the $\pi$ in the numerator cancels the $\pi$ in the denominator, leaving $\dfrac{7\times180}{6} = \dfrac{1260}{6}=210$.

So $\dfrac{7\pi}{6}$ radians $=210^\circ$.

Check (independent route — convert back). $210^\circ\times\dfrac{\pi}{180} = \dfrac{210\pi}{180} = \dfrac{7\pi}{6}$ (dividing numerator and denominator by their HCF $30$), exactly the original value — confirming the answer.

Since $\pi$ rad corresponds to $180^\circ$, first note $\dfrac{7\pi}{6}=\pi+\dfrac{\pi}{6}$, i.e. $180^\circ$ plus one-sixth of $180^\circ$ ($=30^\circ$), giving $180^\circ+30^\circ=210^\circ$ directly, without forming a large fraction.

Forgetting to cancel $\pi$ and leaving an answer that still contains $\pi$ (a degree measure should never contain $\pi$); also miscounting $210^\circ$'s quadrant later in a problem — $210^\circ$ lies in the third quadrant, not the second, since it is between $180^\circ$ and $270^\circ$.