Every Angle for a Tangent
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 45 of 57.
Because tangent repeats every half turn, its angles come in pairs half a turn apart. To list them over an interval, find the first one and keep adding π (or 180°).
Take tan(θ) = 1 on [0, 4π). The first angle is π/4. Adding π again and again gives 5π/4, 9π/4 and 13π/4, and the next, 17π/4, is past 4π. Four angles over two turns: two per turn, as with sine and cosine, but evenly spaced.
Challenge
The circle is labelled in radians. Tap every angle from 0 up to 4π with tan(θ) = -√(3). The Turn buttons above the circle switch to the second turn. 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 Points9Tangent on the Circle
Tangent Is y over xWhere Tangent Is UndefinedTangent in RadiansEvery Angle for a TangentRecap: Tangent