# Radians

## Introduction to Radians

**Basic Concepts and Comparison with Degrees**

- Understand that
**radian**is another way of measuring angles, which is based on the radius of a circle. - Get comfortable with the relationship:
**180 degrees**is equivalent to**π radians**and hence, 1 radian is approximately**57.3 degrees**. - Develop an understanding of why radians are often more practical in mathematics than degrees. This is largely due to their natural division of a circle into equal parts by its radius.

**Conversion between Radians and Degrees**

- Be proficient in converting angles given in degrees into radians and vice versa. A useful rule: multiple the number of degrees by
**π/180**or divide the number of radians by**180/π**to perform the conversions. - Be able to simplify expressions involving pi (π) in radians.

## Properties of Radians

**Circles and Arcs**

- Understand the application of radian measure in finding lengths of arcs in a circle. Learn that an arc length of a circle is
**rθ**, where r is the radius and θ is the angle in radians. - Understand that the area of a sector of a circle is
**1/2 *r²θ**, where r is the radius and θ is the angle in radians.

**Trigonometric Functions and Radians**

- Appreciate that trigonometric functions, i.e., sine, cosine and tangent, are often defined in terms of radians rather than degrees, especially for calculus.
- Recognise the
**unit circle**as a tool for understanding trigonometric functions using radians.

**Real World Applications**

- Understand that radian measure is frequently used in any science involving wave motion, linear and angular speeds and in calculus.
- Be familiar with situations in physics and engineering where radian measure is more practical, specifically in rotational dynamics and simple harmonic motion.

**Graphical Representation**

- Be capable of sketching trigonometric functions with arguments in radians.
- Understand how changing the measure from degrees to radians affects the graphs and the periodicity of sine, cosine and tangent functions.