The Reference Angle
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 3 of 56.
The reference angle is the acute angle between the terminal side and the x axis (0° or 90° when the side lies on an axis). It is what the special values table looks up, since the table only lists angles from 0° to 90°.
Measure it to the nearer half of the x axis. In quadrant II it is 180° − θ, so 135° has reference angle 45°. In quadrant III it is θ − 180°, so 240° has 60°. In quadrant IV it is 360° − θ. Solving an equation runs this backwards: from the reference angle and the quadrant back to the angle.
Challenge
Mark the reference angle of 330°, 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 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 Domain