Finding the Angle
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 22 of 57.
Turn s = rθ round and it gives the angle: θ = s/r, in radians. A swing of radius 8 m whose seat travels 12 m along its arc turns through 12/8 = 1.5 radians.
For degrees, multiply by 180°/π: 1.5×180°/π is about 85.9°. The two steps can share one line: θ = 12/8 × 180°/π.
Sanity check: 1.5 radians is a little less than π/2, about 1.57, so the answer should be a little less than 90°. It is.
Challenge
A pendulum 80 cm long swings along an arc 30 cm long. Find the angle θ it swings through, in degrees. Write θ with the numbers in, then a line with θ 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