Every Turn at Once
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 12 of 57.
A value that occurs once in a turn occurs again in every turn. The height is 1 only at the top, 90°, but over three turns the top is reached three times: at 90°, at 90° + 360°, which is 450°, and at 90° + 720°, which is 810°.
So the angles with a given value come in families, one member per turn. Find the members in the first turn, then add 360° to each, again and again, until you leave the interval you were asked about. Every member of the family is coterminal with the first one.
Challenge
Tap every angle from 0° up to 1080° (three full turns) where the height is −1, sin(θ) = -1. The Turn buttons above the circle move 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 Pizza3Coterminal Angles
Coterminal AnglesBack Into One TurnValues Repeat Every TurnEvery Turn at OnceRecap: Coterminal Angles