Q.The radian measure of $37^\circ 30'$ is :

Use $\pi=180^\circ$: $\tfrac{\pi}{8}=22.5^\circ$, and the $0.5^\circ$ is $30'$, giving $22^\circ 30'$.

Since $\pi$ radians $=180^\circ$,

$\frac{\pi}{8} = \frac{180^\circ}{8} = 22.5^\circ$

Convert the decimal part to minutes using $1^\circ = 60'$:

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Write $37^\circ 30'=37.5^\circ$ and multiply by $\tfrac{\pi}{180}$ to get $\tfrac{5\pi}{24}$.

First express the angle in decimal degrees: $30' = \tfrac{30}{60}^\circ = 0.5^\circ$, so the angle is $37.5^\circ$.

Now use $1^\circ = \dfrac{\pi}{180}$ radians:

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