Every Angle for a Value
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 38 of 57.
To find every angle in one turn with a given value, run the method backwards. The size names the reference angle; the sign names two quadrants.
Take sin(θ) = -√(2)/2. The size √2/2 means reference angle 45°. Sine is negative in quadrants III and IV. In III the angle is 180° + 45° = 225°; in IV it is 360° − 45° = 315°. So two angles, one in each quadrant where the sign fits.
The usual slip is to stop after one angle. Every value strictly between −1 and 1 occurs twice in a turn.
Challenge
Tap every angle in one turn with cos(θ) = -1/2, 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 Pizza8All Four Quadrants
Points in Quadrant IIQuadrants III and IVEvery Angle for a ValuePoints in RadiansExact Values in RadiansRecap: Four Quadrants