Mathematics

Mathematics

Problem

In △ABC\triangle ABC, ∠B=90∘\angle B = 90^{\circ} and ∠A=θ\angle A = \theta. It is given that sin⁡θ=35\sin\theta = \dfrac{3}{5}. Answer the following questions. a. (i) Find csc⁡θ\csc\theta. b. (ii) Calculate cos⁡θ\cos\theta and hence sec⁡θ\sec\theta. c. (iii) Determine tan⁡θ\tan\theta and cot⁡θ\cot\theta. d. (iv) Verify that (csc⁡θ)2−(cot⁡θ)2=1(\csc\theta)^2 - (\cot\theta)^2 = 1 using the values obtained above.

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