Radians Without π
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 17 of 57.
Not every radian measure has π in it. A wheel that turns through 3 radians has turned 3 radius lengths of arc, a little less than a half turn.
To see it in degrees, multiply by 180°/π: 3×180°/π is about 171.9°. Here π does not cancel, so the answer is rounded. The calculator gives 180/π as about 57.2958, the number of degrees in one radian.
A common calculator mistake is typing a radian angle into a calculator set to degrees, or the other way round. sin 3 in radians is about 0.141; in degrees, sin 3° is about 0.052. Always ask which unit the number is in.
Challenge
A wheel turns through 2.5 radians. Write that angle x in degrees: first the conversion, then x rounded to one decimal place, keeping the ° sign. Then press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Angles and the Unit Circle
1A Point on a Circle
Height on the CircleAcross: the CosineSame Height, Two AnglesRecap: Height and Across4Radians
What a Radian IsDegrees to RadiansRadians to DegreesRadians Without πTurns in RadiansRecap: Radians5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza