USE OF LOGARITHMS. 1. Given the sides of a triangle, a= 450.2 ft., b = 430.3 ft., c = 420.1 ft., to calculate the angles A, B, C, by the formulae 2. (a) Calculate amount (A) of $1 at compound interest for 25 years, at the rate of four per cent. per annum, by the formula A = (1.04). (b) Calculate the present value (P) of $1 due 25 years hence, interest considered as in (a), by the formula 3. The volume of a sphere being 500.4 cubic inches, find its diameter. 4. Determine the smallest angle whose logarithmic cotangent is 0.0938 September. 1899 1. Prove the following relations: sin (-x) =- sin x; cos(x) = cos x; cosec (- x) sin x; tan (+x) = tan x; cos (T+x) 2. Express each of the other simple trigonometric functions in terms of sin x. 5. Assuming tan a and tan (m-1) a to be known, derive a formula for expressing the value of tan ma. 6. From the equation a sec2 0 = b + 2 c tan 0, find tan 0. 7. Write the formulae for solving a triangle ABC when two sides, a and b, and the included angle C, are given; and explain briefly their application. Use of Logarithms. 1. Given two sides of a triangle, a = 576.5, b = 555.2, and the angle A (opposite a) = 58° 10. 2. to solve the triangle. Check your work. 2. Find approximately the time it will require for $1 to double itself at compound interest, at the rate of 4 per cent. per annum-using the formula (1.04)* = 2, x being the required time in years. 3. Compute the value of the following expression: 3 0.3756 X 0.265 0.227 4. Determine the smallest angle whose logarithmic cosine is 9.84105—10. ALGEBRA. JUNE, 1899. To QUADRATICS. I. Find the highest common factor of 2x2+4x2 + 2x and 3x+9x2 + 6x. 2. Find the value in its simplest form of 5. A has a hours to spare for an outing. How far can he ride with a friend at the rate of b miles an hour and just consume the time in walking back at the rate of c miles an hour? 6. Extract the square root of x* x-4x2+8x' - 8x +4. 7. Simplify the following expressions: |