Calendar: 1850-1851 Page 372

368 THE SCHOOL II -CrigonomctrD Show that sin sin cos -f- cos sin Find the sines of 30 15 and 18 Prove the formula sin sin sin 2a -sin Show that tan -f tan tan-1 1-ab α2 Prove the formula cos --- supposing to be greater than 90 Given the sides and and the angle in triangle find the perpendiculars let fall from the angles on the opposite sides Explain the method of proportional parts in finding logarithms DIFFERENTIAL CALCULUS Define differential coefficient and from your definition determine '4 the following cases ax χ2 sin -1 log sin Differentiate sin and cos Show that in general the development of -f- can only contain positive and integral powers of Prove the rule for finding the value of vanishing fraction in all its cases Prove the rule for finding maxima and minima Inscribe the greatest isosceles triangle in given circle Trace the curves w2 -Vr 0sin Θ χ Deduce the expression r2 from the expression χ Explain generally the theory of contact of different orders and apply this theory to determine the radius of curvature