Plane Trigonometry, for Colleges and Secondary Schools |
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Page 2
... base a . The latter statement is taken as the definition of a logarithm , and is expressed by mathematical symbols ... base is 2 , what are the logarithms of 1 , 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 ? 4. When the base is 5 , what are the ...
... base a . The latter statement is taken as the definition of a logarithm , and is expressed by mathematical symbols ... base is 2 , what are the logarithms of 1 , 2 , 4 , 8 , 16 , 32 , 64 , 128 , 256 ? 4. When the base is 5 , what are the ...
Page 4
... base ; and to the base chosen there cor- responds a set or system of logarithms . In the common or deci- mal system the base is 10 , and , as will presently appear , this system is a very convenient one for ordinary numerical calcula ...
... base ; and to the base chosen there cor- responds a set or system of logarithms . In the common or deci- mal system the base is 10 , and , as will presently appear , this system is a very convenient one for ordinary numerical calcula ...
Page 11
... base is 6 ft . and the hypotenuse 10 ft . What is the perpendicular ? Calculate the following ratios , viz . : perpendicular hypotenuse base hypotenuse perpendicular base base perpendicular hypotenuse base hypotenuse perpendicular What ...
... base is 6 ft . and the hypotenuse 10 ft . What is the perpendicular ? Calculate the following ratios , viz . : perpendicular hypotenuse base hypotenuse perpendicular base base perpendicular hypotenuse base hypotenuse perpendicular What ...
Page 12
... base is 6 yd . , and the hypotenuse 10 yd . ? When the base is 6 mi . , and the hypotenuse 10 mi . ? When the base is 12 ft . , and the hypotenuse 20 ft . ? When the base is 3 in . , and the hypotenuse 5 in . ? Compare , if possible ...
... base is 6 yd . , and the hypotenuse 10 yd . ? When the base is 6 mi . , and the hypotenuse 10 mi . ? When the base is 12 ft . , and the hypotenuse 20 ft . ? When the base is 3 in . , and the hypotenuse 5 in . ? Compare , if possible ...
Page 14
... base is 30 ft .; find the height . 9. What is the length of the diagonal of a square whose side is 20 ft . ? 10. What is the length of the side of a square whose diagonal is 20 ft . ? N. B. The following examples will be used again for ...
... base is 30 ft .; find the height . 9. What is the length of the diagonal of a square whose side is 20 ft . ? 10. What is the length of the side of a square whose diagonal is 20 ft . ? N. B. The following examples will be used again for ...
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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'.