Exact values beyond one revolution

Angles are measured from the positive horizontal axis; anticlockwise is positive. Add or subtract whole turns, 360 or 2pi, to locate the terminal ray. Use its reference angle and quadrant signs. A right isosceles triangle with legs 1 gives sin45 =cos45 =1/ 2. Halving an equilateral triangle with side 2 gives sin30 =1/2 and cos30 = 3/2. These determine the reciprocal values too. Reduce the angle to one turn; locate its quadrant or axis; choose the exact acute-angle magnitudes; attach signs; take reciprocals only when allowed. Sine and cosecant share a sign, cosine and secant share a sign, tangent and cotangent share a sign. For theta=-7pi/6, add 2pi to obtain 5pi/6. Thus sintheta=1/2, costheta=- 3/2, tantheta=-1/ 3, cosectheta=2, sectheta=-2/ 3, cottheta=- 3. A negative angle need not have negative sine: the terminal quadrant decides. On an axis, use the coordinates rather than an acute reference angle. Keep sectheta=1/costheta distinct from the inverse-function notation cos-1x.