You Can Do Math

Radians are the preferred unit that mathematicians and scientists use for measuring angles. Likewise steradians are the preferred unit used for measuring solid angles. This book explains the key concepts behind radians and steradians, as well as how to perform mathematical calculations based on these units (including many worked examples, questions for you to do yourself, and answers to those questions to check your results).

Topics covered in the book include:

• Key terminology associated with circles
• A comparison between measuring angles in degrees and other units such as gradians
• The definition of radians
• How angles can be measured in radians
• Why radians are a "natural" unit for measuring angles
• How many radians correspond to a full circle rotation, half circle rotation, and a quarter circle rotation (right angle)
• How many degrees correspond to a radian
• How to convert degrees into radians
• How to convert radians into degrees
• Conversions of some common angles between degrees and exact radian values
• How to calculate arc lengths using radians
• How to calculate sector perimeters using radians
• How to calculate sector areas using radians
• How to calculate chord lengths using radians
• How to calculate segment perimeters using radians
• How to calculate major and minor segment areas using radians
• Radians usage as an SI Unit
• Some uses of radians in physics
• Common SI Unit prefixes of radians, and subject areas where you may encounter them
• Milliradian approximations used in various militaries and in gunnery
• Dimensional analysis involving radians
• The definition of steradians
• How many steradians are in a complete sphere and in a hemisphere
• How to calculate the aperture angle of a cone of 1 steradian
• Some common applications of steradians
• Dimensional analysis involving steradians