arctan, Rounded
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 12 of 56.
arctan takes any number. arctan(3) is 71.565°, so 71.6° to one place: a tangent of 3 is a steep line, and the angle is close to 90° without reaching it.
A negative input gives an angle below the axis, turning clockwise: arctan(−0.5) is −26.565°, so −26.6°. As with arcsin, arctan(−c) = −arctan(c). The answer is not 333.4°, even though that angle has the same tangent: it is outside (−90°, 90°).
Challenge
Work out x = arctan(−2.5) in degrees, to one decimal place. Write x ≈ …°, with the degree sign, as a new line, then press Check.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Trig Equations and Inverses
1Your First Trig Equations
One Equation, Two AnglesReading Signs on the CircleThe Reference AngleRecap: First Equations4Compositions
Draw the TriangleThe Outer FunctionA Negative InsideWhen Undoing Does Not UndoRecap: Compositions2Inverses and Their Ranges
Why arcsin Gives One AngleNegative Inputs to arcsinThe Range of arccosThe Range of arctanRecap: Inverse Ranges5Equations on a Domain
A Negative CosineTangent EquationsEquations in RadiansTwo Turns, Four AnswersRecap: On a Domain3Evaluating Inverse Trig
Rounded Angles in DegreesRounded Angles in Radiansarctan, RoundedAn Angle From a SlopeRecap: Inverse Values