Values Repeat Every Turn
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 11 of 57.
Coterminal angles end at the same point of the circle, so they have the same height and the same across. That means sin(θ + 360°) = sin(θ), and the same for cosine: the values repeat every turn.
Take sin(390°). One turn less is 30°, so sin(390°) = sin(30°), which is one half. Negative angles work the same way: cos(-360°) = cos(0°), which is 1.
On the board, the chip Subtract 360°, one full turn takes off one turn and leaves the value unchanged. Press it until the angle is inside one turn, then work the value out.
Challenge
Work out sin(810°) exactly: take off full turns with the chip, then work the value out. Then press Check.
Try it yourself
Simplify the expression
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