Signs by Quadrant
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 32 of 57.
The quadrant decides the signs. cos θ is the across, so it is positive right of the y-axis (quadrants I and IV). sin θ is the height, positive above the x-axis (I and II). Tangent is sine over cosine, tan(θ) = sin(θ)/cos(θ), so it is positive where the two agree: quadrants I and III.
In quadrant II the point is left and up: cos −, sin +, so tan −. One mnemonic, of several, for which function is positive where: All Students Take Calculus, counterclockwise from quadrant I. All three are positive in I, only Sine in II, only Tangent in III, only Cosine in IV.
Challenge
Choose the sign of sin, cos and tan for every angle in quadrant IV, 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