Signs at Any Angle
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 34 of 57.
For an angle outside 0° to 360°, find where it ends first, then read the signs from the quadrant. Take 480°: one turn less is 120°, quadrant II, so sine is positive and cosine and tangent are negative.
Negative angles are the same. −60° turns clockwise into quadrant IV: cosine positive, sine and tangent negative. Nothing about the sign depends on how the angle got there, only on where its side stops.
On an axis one of sine and cosine is 0, which has no sign, and tangent is 0 or undefined. That is why a sign question always uses an angle inside a quadrant.
Challenge
Choose the sign of sin, cos and tan at -135°, 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: 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