Mathematics

Mathematics

Problem

Answer the following questions about the signs and magnitudes of trigonometric ratios for angles in different quadrants. a. (i) State the fundamental relationship between sin⁡θ\sin\theta and cos⁡θ\cos\theta that holds for every real θ\theta. b. (ii) Explain why, if sin⁡θ>0\sin\theta>0 and cos⁡θ<0\cos\theta<0, the angle θ\theta must lie in the second quadrant and tan⁡θ\tan\theta is negative. c. (iii) For an angle θ\theta in the third quadrant with sin⁡θ=−k\sin\theta=-k where 0<k<10<k<1, express cos⁡θ\cos\theta and tan⁡θ\tan\theta in terms of kk and justify the sign of each ratio.

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