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You Can Do Math: Radians and Steradians
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
