SEPTEMBER 1891.. 1. Express an angle of 3° in radians. 2. Write the simplest equivalent expressions for; cos (+), sin (7+), tan (11⁄2π — ). 3. Express tan 9, sec 9, and and cos ø, respectively in terms of sin 9. 4. Given tan 9 = (b÷ a); find the value of, a cos 29 + b sin 29. 5. Derive the formula cos 1⁄2ß = 6. Show that if ( sin 29, = sin 20. I + cos B 2 0) = 1⁄2, then cos (+0) = 7. Given two sides of a triangle, 450.36 ft. and 475.28 ft., and the included angle, 65° 25′.2, to find the remaining parts of the triangle. (π JUNE 1892. 1. Express an angle of 1.5 radians in degrees. 2. Write the simplest equivalents for sin (π † 0), sin (11⁄27 + 0), tan (11⁄2 π Ø), tan (27 π 3. Express sin and sec in terms of tan 0. 4. Derive the formula for cos (+) in terms of the sines and cosines of d and 0. 5. Derive the formula sin 20 = 2 sin 0 cos 0. 6. Show that tan (+8) = tan (4π 6). 2 tan 26. 225.4, 7. The three sides of a triangle are as follows: a b = 231.5, c = 242.8; find the angles, and verify the correctness of your work. SEPTEMBER 1892. 1. Express an angle of 60° in radians. 2. Represent geometrically the different trigonometrical functions of an angle. State the signs of each function for each quadrant. 3. Express tan 0 and sec ℗ in terms of sin (. 4. Derive the formula sin λ + sin d 2 sin (+8) cos 1⁄2 (λ — 8). 5. Show that, if a, b, and c, are the sides of a triangle, and A is the angle opposite the side a, then a2 = b2 + c22bc cos A. 6. Given cos 2x = 2 sin x, to find the value of sin x. 7. Given two sides of a triangle, a = 450.2, b = 425.4, and their included angle C = 62° 8', to find the remaining parts of the triangle. JUNE 1893. 1. Express an angle of 15° in radians. 2. Write the simplest equivalents for sin (π + 4), tan (2π- ), cos (11⁄2 π - P), sec (π + 9). 3. Express (a) tan 9 in terms of sin , cos 9, and cot 9, respectively, and (b) cos p in terms of tan 9, sec 9, and cosec, respectively. 4. Show (a) that sin (a + B) + sin (a) 2 sin a cos B. (b) that cos (a + B) + cos (a — ß) = 2 cos a cos B. b2 + c2 — a3 5. Assume the formula cos α = 2bc and show 6. Obtain a formula for tan 20 in terms of cos 0. 7. The base of a triangle c = 556.7, and the two adjacent angles A = 65° 20′.2, B = 70° oo'.5; calculate the area of the triangle. 8. Given o < a < 90°, and log cos a = 1.85254, to determine a. SEPTEMBER 1893. 1. Reduce an angle of 3.5 radians to degrees. 2. Define the different trigonometrical functions of an angle and give their algebraic signs for an angle in each quadrant. 3. Write simple equivalents for the following functions: sin(); cos (-); tan (1⁄2π + ); sec (11⁄2 — ). 4. Express cosec in terms, respectively, of sin e, cos 0, tan 0, cot 0, and sec 0. sin a sin ) + (sina cosd + 5. Reduce (cos a cos d cos a sin d) to its simplest equivalent. π 6. Show that tan Ꮎ = 4 I tan e 7. The sum of two sides, a and b, of a triangle is 546.7 ft., the sum of the opposite angles, A and B, is 124°, and the ratio sin A: sin B = 1.003; determine the angles and sides of the triangle. 8. Given o <λ < 90°, and log cot A = 0.03293, to determine A. |