Q.Convert $75^\circ$ into radian measure.

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

$75^\circ = 75\times\dfrac{\pi}{180} = \dfrac{75\pi}{180} = \dfrac{5\pi}{12}$ radians.

Step 1 — recall the conversion relation. Since one full rotation is both $360^\circ$ and $2\pi$ radians, half a rotation gives $180^\circ=\pi$ radians, so $1^\circ=\dfrac{\pi}{180}$ radians.

Step 2 — apply it. $75^\circ = 75\times\dfrac{\pi}{180}$ radians $= \dfrac{75\pi}{180}$ radians. Cancelling the HCF $15$ from numerator and denominator: $\dfrac{75\pi}{180}=\dfrac{5\pi}{12}$.

So $75^\circ = \dfrac{5\pi}{12}$ radians.

Check (independent route — convert back). $\dfrac{5\pi}{12}$ radians $= \dfrac{5\pi}{12}\times\dfrac{180^\circ}{\pi} = \dfrac{5\times180}{12}^\circ = \dfrac{900}{12}^\circ = 75^\circ$, exactly the original angle — confirming the conversion is correct.

Alternatively, split $75^\circ = 60^\circ+15^\circ$, convert each piece separately ($60^\circ=\pi/3$, $15^\circ=\pi/12$) and add: $\pi/3+\pi/12 = 4\pi/12+\pi/12=5\pi/12$ — the same result, useful as a mental check when a calculator isn't at hand.

A common slip is multiplying by $180/\pi$ instead of $\pi/180$ when going from degrees to radians (the two factors are reciprocals of each other and easy to swap); another is forgetting to simplify the resulting fraction, leaving an unreduced form like $75\pi/180$ instead of $5\pi/12$.