Mathematics

Mathematics

Problem

In right-angled triangle ABC with right angle at C, let ∠A=θ\angle A = \theta. a. (i) Express sin⁡θ\sin \theta and cos⁡θ\cos \theta in terms of the sides of ΔABC\Delta ABC. b. (ii) Write sin⁡(90∘−θ)\sin(90^\circ - \theta) in terms of the sides and hence show that sin⁡(90∘−θ)=cos⁡θ\sin(90^\circ - \theta) = \cos \theta. c. (iii) Using θ=37∘\theta = 37^\circ, verify numerically, correct to four decimal places, that sin⁡(90∘−θ)\sin(90^\circ - \theta) equals cos⁡θ\cos \theta.

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