SEPTEMBER 1885. 1. Give the algebraic signs of the different trigonometrical functions for an angle terminating in each of four quadrants. 2. Express the sine, tangent, and secant of 11⁄2π functions of a. 3. Find the value of tan in terms of sin 9. -- a in 5. a, b, c, being the sides of the triangle ABC respectively opposite the angles A, B, and C, show that, 2575 ft., 6. In the triangle ABC, given the sides BC AC JUNE 1886. 1. Explain the rule of sines for angles. Is there any limit to the value of an angle as considered in trigonometry? Express an angle of 23 (of a radian) in degrees. When we speak of an angle nz (n being any number) what is understood to be the unit of measure? 2. Explain how the sine and tangent of an angle vary as the angle varies from o to 27. 3. Prove the following formulae: sin (-a) sin a; tan a; tan (1⁄2 π + α) 4. Express sin a and cos a in terms of tan a; also, tan a in terms of sin a and cos a respectively. 5. Given sin (9 + B) = cos (P B) to find . 6. Find, with the help of the tables, all the angles be. tween o° and 360° whose cosine = 0.27. 7. In the triangle ABC, given A= 43° 27.3′, B = 46° 32.7, AC 4056.5, to find the remaining parts. SEPTEMBER 1886. 1. (a) Find by means of the Tables the cosine and tangent of 317°.3. (b) Determine all the angles between o and 47 whose cosine is 2; also those whose cosine is 2. Given sin in terms of b. 12. b, to express cos B, tan B, cot ẞ, sec ß, 3. Deduce the formula sin x + sin y = 2 sin 1⁄2(x + y) cos (xy) and derive from it sin x 2(x+y) sin 1⁄2 (x − y). sin y 2 Cos 4. Given the sum of two angles and the ratio of their sines to explain a method for determining the angles. 5. Find an expression for the cosine of an angle of a triangle in terms of the sides of the triangle. 6. Solve the triangle ABC, having given AB 53.94. BC= 156.5, B = 15° 13′.2. JUNE ISSS. I. Find how many degrees there are in an arc whose radius is one foot, and whose length is 0.1 foot? 3. Given sin ß = 0.1 to find cos B, tan B, cot B, sec ß, sin 2, and cos 25. 4. Given tan 0.1 to find tan 2. 6. Given two sides of a triangle a 575, b = 425, and the angle A opposite the former maining parts of the triangle. 125° 30', to find the re 7. The sine of a certain angle of a triangle is 0.67559 and its cosine is 0.73728; find the angle. SEPTEMBER 1888. 1. Find the length of an arc of 90° in a circle whose radius is one foot. 2. Give the algebraic signs of the sine, tangent, and secant of the following angles, cosec (—), tan ß, cot ß, sin 2ß, tan 2ß. 5. Given sin (x + a) + cos (x + α) cos (x a), to find x. sin (xa) + 6. Find the angles of a triangle ABC when A = 10° 30′, and 5AB = 8AC. |