Any Circle, Any Radius
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 47 of 57.
On a circle of radius r the picture is the unit circle scaled by r. Every length grows by the same factor, so the point at angle θ is (r cos θ, r sin θ).
On a circle of radius 6 the point at 240° has x = 6cos(240°) and y = 6sin(240°). 240° is in quadrant III with reference angle 60°, so cos(240°) = -1/2 and sin(240°) = -√(3)/2. The point is (-3, -3√(3)).
A seat on a wheel or the tip of a fan blade is tracked the same way: the centre is the origin, the radius scales the unit circle, the angle picks the point.
Challenge
A Ferris wheel of radius 20 m is centred at the origin. A seat sits at 150°, measured counterclockwise from the 3 o'clock position. Find its coordinates exactly: write a line x = ... and a line y = ..., with any root in simplest form and no decimals. 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: Radians7Reference Angles and Signs
Reference AnglesReference in III and IVSigns by QuadrantSign and SizeSigns at Any AngleRecap: Reference Angles10Six Functions, Any Circle
Any Circle, Any RadiusFrom a Point to the AngleSecant, Cosecant, CotangentReciprocals in RadiansRecap: Six Functions5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza