Sign and Size
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 33 of 57.
Every exact value comes from two questions. Size: the reference angle names the special triangle under the point, and that gives the value without its sign. Sign: the quadrant.
Take cos(135°). 135° is in quadrant II with reference angle 45°, so the size is cos(45°), √2/2, and the cosine is negative in quadrant II: cos(135°) = -cos(45°), which is −√2/2.
On the board the chip Use the reference angle 45° turns cos 135° into −cos 45°, sign included, and the note under the line names the quadrant. Then work out the value at the reference angle. In this lesson the board will not turn cos 135° into a value in one press.
Challenge
Work out cos(210°) exactly: use the reference angle, then the value. Then press Check.
Try it yourself
Simplify the expression
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: Radians7Reference Angles and Signs
Reference AnglesReference in III and IVSigns by QuadrantSign and SizeSigns at Any AngleRecap: Reference Angles5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza