Plane Trigonometry, for Colleges and Secondary Schools |
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Page 2
... equal N. For some purposes , this idea is presented in these words : If a = N , then x is the logarithm of N to the base a . The latter statement is taken as the definition of a logarithm , and is expressed by mathematical symbols in ...
... equal N. For some purposes , this idea is presented in these words : If a = N , then x is the logarithm of N to the base a . The latter statement is taken as the definition of a logarithm , and is expressed by mathematical symbols in ...
Page 3
... equal to the sum of the logarithms of the factors . ( 2 ) The logarithm of the quotient of two numbers is equal to the logarithm of the numerator diminished by the logarithm of the denominator . ( 3 ) The logarithm of the rth power of a ...
... equal to the sum of the logarithms of the factors . ( 2 ) The logarithm of the quotient of two numbers is equal to the logarithm of the numerator diminished by the logarithm of the denominator . ( 3 ) The logarithm of the rth power of a ...
Page 4
... equal to th of the logarithm of the number . Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and division are replaced by those ...
... equal to th of the logarithm of the number . Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and division are replaced by those ...
Page 13
... equal to the sum of the squares of the measures of the other two sides . ( b ) The ratio of the length of any circle to its diameter is a number which is the same for all circles . * The exact value of this ratio is incommensurable and ...
... equal to the sum of the squares of the measures of the other two sides . ( b ) The ratio of the length of any circle to its diameter is a number which is the same for all circles . * The exact value of this ratio is incommensurable and ...
Page 15
... equal to 39.37 . . . inches . * Drawing to scale . It is often desirable to have a drawing on paper which shall serve to give an accurate idea of the relations of certain lines and positions . Maps and architects ' plans are familiar ...
... equal to 39.37 . . . inches . * Drawing to scale . It is often desirable to have a drawing on paper which shall serve to give an accurate idea of the relations of certain lines and positions . Maps and architects ' plans are familiar ...
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Common terms and phrases
A+B+C acute angle algebraic angle of elevation central angle CHAPTER circle circumscribing cologarithm column computation cos² cosec cotangent deduced denoted Derive draw equal equation EXAMPLES expression figures find log Find the angle Find the distance Find the height find the number formulas geometrical Given log graph Hence Hipparchus hypotenuse inverse trigonometric functions isosceles triangle law of sines length M₁ mantissa mantissa of log mathematics method negative NOTE number of degrees number of sides OP₁ perpendicular proj Prove radian measure radius regular polygon revolving right angles right-angled triangle sec² secant Show shown sin² sin³ sine and cosine Solve spherical trigonometry subtended tan-¹ tan² tangent terminal line theorems tower triangle ABC trigono trigonometric functions trigonometric ratios turning line whole number X₁
Popular passages
Page 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.
Page 54 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.
Page 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Page vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.
Page 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.
Page 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Page 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Page 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.