Turns in Radians
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 18 of 57.
In radians a full turn is 2π, so coterminal angles differ by multiples of 2π instead of 360°. π/4 and 9π/4 end on the same side, because 9π/4 - 2π = π/4.
That makes repeating values easy to list. The height is −1 only at the bottom of the circle, 3π/2. In the second turn the bottom is reached again at 3π/2 + 2π, which is 7π/2. Each turn adds one more member to the family.
The sizes of the special angles in radians are worth knowing by sight: 30° is π/6, 45° is π/4, 60° is π/3, 90° is π/2.
Challenge
The circle is labelled in radians. Tap every angle from 0 up to 4π (two turns) where the height is one half, sin(θ) = 1/2. The Turn buttons above the circle switch between turns. 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