Answer the following questions about the signs and magnitudes of trigonometric ratios for angles in different quadrants.
(i) State the fundamental relationship between sinθ and cosθ that holds for every real θ.
(ii) Explain why, if sinθ>0 and cosθ<0, the angle θ must lie in the second quadrant and tanθ is negative.
(iii) For an angle θ in the third quadrant with sinθ=−k where 0<k<1, express cosθ and tanθ in terms of k and justify the sign of each ratio.