# Calendar: 1878-1879 Page 596

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5'J4 GENERAL LITERATURE AND 8CIENCE Express cosz '1 71 being odd in terms of the cosines of multiples of Obtain the exponential values of sin θ and cos If cos φ cosa -f- sin shew that sin2 θ sin Find the general value of tan sin cos 10 tangent to circle cuts diameter produced at an angle 2Θ Shew that the portion of the diameter intercepted without the circumference is equal to tan Sf tan θ where is the diameter 11 Define the polar triangle and prove the relations which exist between the sides and angle of triangle and its polar triangle 12 In spherical triangle prove that cos ens cos cos ---- sinb sine tan-2 -v C0V cos XXIII -tgromrtrp To describe parallelogram that shall be equal to given triangle and have one of its angles equal to given rectilineal angle To divide given straight line nto two parts so that the rectangle contained by the whole and one of the parts may be rqual to the square on the other part The angles in the same segment of circle are equal to one another

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