# Calendar: 1899-1900 Page 758

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cvi FACULTY OF SCIENCE Apply it to solve the following question The value of an article depreciates per cent every year If it is now worth sovereign find to the nearest penny its value 10 years ago Define Logarithm and shew that 10ga χ -f ogay 10ga xy If xyi-m and xy find to places of decimals the values of χ and Define the tangent of an angle Trace the changes in sec tan as increases from to 360 Prove that tan cot Θ tan θ cot θ sec 2Θ cosec 20 sec 2Θ -f cosec 2Θ ii cos θ cos φ sin θ sin φ sin θ φ £ sin 20 8ίη2φ tan2 10 Prove the formula cos Λ -- ד tan2 If cos2 10 sin4 c2 and y-fl prove that sin2 C- 11 Investigate an expression for the area of triangle in terms of one side and the adjacent angles If the altitude of triangle is half the base shew that the sine of the vertical angle is twice the product of the sines of the two base angles 12 and Β are two lighthouses ship Ρ due east of observes the angle ABB to be φ After steaming northward to until lies due south-west the angle AQB is observed to be ψ Shew that the line AB makes with due north an angle tan-1 -f cot ψ cot φ cot ψ where φ is measured to the north of west IV Patfjemattcg Stfifcer Paper YEARS II III Γ '- 'I ll'lf'ljl י י י י If two straight lines are cut by parallel planes prove that they are cut in the same ratio

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