Exact Values in Radians
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 40 of 57.
The board works the same in radians. Take sin(7π/6). 7π/6 is π + π/6: quadrant III, reference angle π/6. Sine is negative there, so sin(7π/6) = -sin(π/6), which is −1/2.
If radians still feel foreign, convert: 7π/6 is 210°. But the quicker habit is to read the fraction: compare the numerator with the denominator to see how far past π or short of 2π the angle goes.
On the board the chip reads Use the reference angle π/6; press it, then work out the value at the reference angle.
Challenge
Work out cos(11π/6) 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: 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