**Example 1: **

Convert $120^{\circ}$ to radian

**Solution: **

**Step 1:** Pen down the angle in degrees to be converted to radians $120^{\circ}$.

**Step 2:** Multiply the number of degrees to be converted by $\frac{pi}{180}$.

$120^{\circ}\ \times$ $\frac{p}{180}$

**Step 3:** Carry out the multiplication process, which is finding out the product.

$120^{\circ}\ \times$ $\frac{p}{180}$ = $120$ $\frac{p}{180}$

**Step 4:** Simplify to the lowest term of the fraction. As both $120$ and $180$ are divisible by $60$, both the numerator and denominator is divided by $60$ to bring it to the lowest term.

$\frac{(\frac{120 p}{180})}{(\frac{60}{60})}$ = $2$ $\frac{p}{3}$

Therefore, $120^{\circ}$ converted to radian is $2$ $\frac{p}{3}$.

**Example 2:**

Convert $\frac{Pi}{3}$ radian to degrees.

**Solution: **

**Step 1:** Pen down the angle in radian to be converted to degrees.

$\frac{Pi}{3}$ radian

**Step 2:** Multiply the number of degrees to be converted by $\frac{180}{pi}$.

$\frac{Pi}{3}$ $\times$ $\frac{180}{pi}$

**Step 3:** Carry out the multiplication process, which is finding out the product.

$\frac{Pi}{3}$ $\times$ $\frac{180}{pi}$ = $60^{\circ}$

Therefore, $\frac{pi}{3}$ radian converted to degrees gives us $60^{\circ}$.

**Example 3:**

Convert $45$ degrees into radian and $\frac{Pi}{6}$ radian into degrees.

**Solution: **

Degree to radian conversion is done by multiplying with $\frac{Pi}{180}$. So, $45^{\circ}$ would be $45\ \times$ $\frac{Pi}{180}$ = $\frac{Pi}{4}$ radian.

Radian to degree conversion is found out by multiplication with $\frac{180}{Pi}$. So, $\frac{Pi}{6}$ radian would be $\frac{Pi}{6}$ $\times$ $\frac{180}{Pi}$ = $30^{\circ}$.