**Give the definition of a radian. Prove that \(1^\circ < 1^c\)** (where \(1^c\) denotes 1 radian)

Q.**Give the definition of a radian. Prove that \(1^\circ < 1^c\)** (where \(1^c\) denotes 1 radian)

**Radian:** The angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle is called 1 radian. \[ 180^\circ = \pi^c \] So, \[ 1^\circ = \left(\frac{\pi}{180}\right)^c = \left(\frac{22}{7 \times 180}\right)^c \] Since \[ \frac{22}{7 \times 180} < 1 \] Therefore, \[ 1^\circ < 1^c \quad \text{(Proved)} \]