Allyn and Bacon, 1899 - Plane trigonometry - 91 pages
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Elmer a. (Elmer Adelbert) 1861 Lyman,Edwin C. (Edwin Charles) 1865 Goddard
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acute angle algebra angle base c.d. Log c.d. Log.Tan Nat called changes characteristic Check colog column complete computations considered corresponding Cos Log cos² cosecant Cot Log Cot Nat cotangent curve decimal depends determined difference distance draw elevation equal equation EXAMPLES Express figures Find Find the height formed formulę four functions given greater Hence increases involved length logarithm mantissa means measure miles minute negative object observed opposite passes perpendicular positive possible principles problems produced Prove quadrant radians radius ratios relations right angle sec² secant Show side Sin Log sin² sine sine and cosine single solution Solve student tables tan² tangent terminal line tions triangle of reference trigonometric trigonometric functions true unit values varies Verify whence
Page 42 - A logarithm is the exponent of the power to which a fixed number, called the base, must be raised to produce a given number.
Page 70 - SINES. In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Page 52 - ... 25 ft. long, leans against a house and reaches to a point 21.6 ft. from the ground. Find the angle between the ladder and the house, and the distance the foot of the ladder is from the house. Why are we able to solve an example like this by trigonometry when we are not able to do so by geometry ? 9. The Washington Monument is 555 ft. high. How far apart are two observers 555 who from points due west of the monument observe its angles of elevation to be 25° and 48° 17
Page 42 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 84 - A ^Vl -sin 4. 4. Remove the ambiguous signs in Ex. 3 when A is in turn an angle of each quadrant. 5. A wall 20 feet high bears S. 59° 5' E. ; find the width of its shadow on a horizontal plane when the sun is due S. and at an altitude of 60°. 6. Solve sin x + sin 2 x + sin 3 x — 1 + cos x + cos 2 x. 7. Prove tan-1 i + tan-1 i = ^ 8.
Page 4 - O or small, be divided into 360 equal arcs, each arc is called a degree. The degree is divided into 60 minutes, and the minute into 60 seconds. The length of a degree, minute, or second, depends on the size of the circle.
Page 11 - The student must notice that sin a is a single symbol. It is the name of a number, or fraction, belonging to the angle a ; and if it be at any time convenient, we may denote sin a by a single letter, such as o, or x. Also, sin2...
Page 6 - What is the measure of a ton when a weight of 10 stone is the unit ? (4) The length of an Atlantic cable is 2300 miles and the length of the cable from England to France is 21 miles. Express the length of the first in terms of the second as unit.
Page 29 - Art. 16 expresses the functions of «, whatever be its magnitude, in terms of each of the other functions of that angle if the ± sign be prefixed to the radicals. The definitions of the trigonometric functions (Art. 12) apply to angles of any size and sign, but it is always possible to express the functions of any angle in terms of the functions of a positive acute angle. The functions of any angle...