Across: the Cosine
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 2 of 57.
The height is one coordinate of the point. The other is how far it sits right or left of the y-axis, its x coordinate, and that one is the cosine of θ, cos(θ). Right of the y-axis it is positive, left of it negative.
P is left of the y-axis, so cos θ is negative; it is above the x-axis, so sin θ is positive.
Together the two coordinates name the point: on the circle of radius 1, the point turned through θ is (cos(θ), sin(θ)). At the start it is (1, 0), so cos(0°) = 1. A quarter turn later it is at the top, straight above the centre, neither left nor right: the point at 90° is (0, 1), so cos(90°) = 0 and sin(90°) = 1.
Challenge
The point has turned through 180°. Set its x and y coordinates, cos(180°) and sin(180°): for each, choose a sign (+ or −) and a size. 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