Calendar: 1860-1861 Page 486

general literature and science 487 Explain why sin determined from sin admits four values Find all the values of sin j- -j- -1 η being an integer The length of path in which the ascent is foot in from the foot of mountain to the top is miles What will be the length of circuitous path in which the ascent is foot in Find the values of θ in the following equations sin 20 sin230 cos m6 cos ηθ If the tangents of the angles of triangle be as the numbers find them and show that if be the sides of the triangle and pv pit ps the perpendiculars on the sides drawn from the opposite angles then j0j P2P3 ab Given the perimeter side and the opposite angle of triangle find the other angles Ex Perimeter 300 feet side 100 feet opposite angle 60 10 Find in terms of the sides of triangle the radius of circle described about it and show what the expression becomes when the triangle is right angled 11 piece of paper mile in length is rolled into solid cylinder find approximately the diameter of he cylinder sup- posing 240 leaves of such paper to have thickness of one inch 12 In segment of circle whose radius is and length of arc circle is inscribed touching the middle point of the arc show that the radius of the circle which touches the arc and chord of the segment and also the inscribed circle is sin2- 13 Find the value of sin θ in terms of cos θ and sin Θ 14 Sum the series sin2 θ sin2 2Θ sin2 θ to η terms