Points Off the Table
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 28 of 57.
Most angles are not 30°, 45° or 60°, and their points have no tidy exact coordinates. They are still (cos θ, sin θ), and a calculator in degree mode gives them.
The point at 20° is (cos 20°, sin 20°). The calculator reads 0.93969 and 0.34202, so to three decimal places the point is (0.940, 0.342). Check that it is on the circle: 0.940² + 0.342² is 1.0006, as close to 1 as rounding allows.
Round only at the end, and give each coordinate the places asked for. A wrong mode still gives numbers between −1 and 1, so check the picture instead: the point at 20° is near the x-axis, so its across must be close to 1. In radian mode cos 20 is about 0.408.
Challenge
Find the point (x, y) at 72° on the unit circle. Write a line for each coordinate, then a line for each rounded to three decimal places. 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 Angles6The Unit Circle
Why (cos θ, sin θ)The 30° and 60° PointsThe 45° PointPoints Off the TableRecap: Quadrant I Points