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How are degrees converted to radians?

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Diagram of a right triangle labeled with sides a, b, and hypotenuse c, alongside formulas for the six trigonometric functions-sine, cosine, tangent, cosecant, secant, and cotangent-each defined by ratios of the triangle's sides. — trigonometry Based on the definitions, various simple relationships exist among the functions. For example, csc A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A, and tan A = sin A/cos A.

To convert an angle from degrees to radians, you use the relationship between the two units of measure. Since a complete revolution is equal to both 360° and $2 π$ radians, it follows that 180° is equal to $π$ radians.12

To perform the conversion, multiply the degree measure by the factor $\frac{π}{180}$ :

$radians = degrees \times \frac{π}{180}$

For example, to convert 90° to radians:
$90 \times \frac{π}{180} = \frac{π}{2} radians$

The radian is considered the most convenient unit for theoretical work in trigonometry because it is defined by the angle at the centre of a circle that intercepts an arc equal in length to the radius.1