Answer the following questions about determining trigonometric ratios from a single known ratio.
(i) Explain why knowing the quadrant of an angle is essential when deducing the remaining trigonometric ratios from one given ratio.
(ii) Illustrate your explanation by taking an angle θ for which sinθ=53 and comparing the values of cosθ when θ is in the first quadrant and when it is in the second quadrant.
(iii) For each of the two cases in part (ii), write down all six trigonometric ratios of θ.