11.2 Converting Radians and Degrees

Degrees and radians are two units for measuring angles. 1 radian is equal to approximately 57.3 degrees. To convert degrees to radians, use the formula: radians = degrees × (π/180).

The length of an arc (L) can be calculated using the formula: L = rθ, where r is the radius and θ is the angle in radians.

To convert radians to degrees, use the formula: degrees = radians × (180/π).

π radians is equal to 180 degrees.

90° is equal to $$\frac{\text{π}}{2}$$ radians.

180° is equal to $$\text{π}$$ radians.

360° is equal to $$2\text{π}$$ radians.

The length of the intercepted arc is 1 unit.

285° is equal to $$\frac{19\text{π}}{12}$$ radians.

-520° is equal to $$-\frac{26\text{π}}{9}$$ radians.