Answer all parts related to the signs of trigonometric ratios.
(i) State the unit–circle definitions of sinθ and cosθ for an angle θ measured from the positive x–axis.
(ii) Using the signs of the abscissa and ordinate in each quadrant, explain how the signs of sinθ and cosθ vary with the quadrant in which θ lies.
(iii) Hence, justify why tanθ is positive in Quadrants I and III but negative in Quadrants II and IV.
(iv) Give one numerical example (an angle in degrees) from each quadrant to illustrate your explanation and list the corresponding ordered pair (cosθ,sinθ). Verify the sign conventions in each case.