Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
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Página 21
... cotangent of the angle A ; is called the secant of the angle 4 ; AM AP MP is called the cosecant of the angle A. These six ratios are known as the trigonometric ratios of the angle A. According to the definition of a ratio ( Art . 8 ) ...
... cotangent of the angle A ; is called the secant of the angle 4 ; AM AP MP is called the cosecant of the angle A. These six ratios are known as the trigonometric ratios of the angle A. According to the definition of a ratio ( Art . 8 ) ...
Página 22
... cotangent were first employed by Edmund Gunter ( 1581-1626 ) , professor of astronomy at Gresham College , London , who made the first table of logarithms of sines and tangents , published in 1620 , and introduced the Gunter's chain now ...
... cotangent were first employed by Edmund Gunter ( 1581-1626 ) , professor of astronomy at Gresham College , London , who made the first table of logarithms of sines and tangents , published in 1620 , and introduced the Gunter's chain now ...
Página 26
... cotangent , and cosecant decrease . Test this conclusion by an inspection of a table of Natural ratios . 3. Find by tables , sin 17 ° 40 ' , sin 43 ° 25 ' 10 " , sin 76 ° 43 ' , sin 83 ° 20 ′ 25 ′′ , cos 72 ° 40 ' 30 " , tan 37 ° 40 ...
... cotangent , and cosecant decrease . Test this conclusion by an inspection of a table of Natural ratios . 3. Find by tables , sin 17 ° 40 ' , sin 43 ° 25 ' 10 " , sin 76 ° 43 ' , sin 83 ° 20 ′ 25 ′′ , cos 72 ° 40 ' 30 " , tan 37 ° 40 ...
Página 29
... cotangent s ; ( 5 ) whose secant is ; ( 6 ) whose cosecant is ? is α a a b 12. A ladder 32 ft . long is leaning against a house , and reaches to a point 24 ft . from the ground . Find the angle between the ladder and the wall . 13. A ...
... cotangent s ; ( 5 ) whose secant is ; ( 6 ) whose cosecant is ? is α a a b 12. A ladder 32 ft . long is leaning against a house , and reaches to a point 24 ft . from the ground . Find the angle between the ladder and the wall . 13. A ...
Página 33
... sec A = 1 ; } ( 1 ) ( c ) tan A 1 1 = cot A = cot A ' or , tan A cot A = 1 . tan A B. The tangent and cotangent in terms of the sine 16-18 . ] 33 RELATIONS BETWEEN RATIOS . Relations between the trigonometric ratios of an acute angle.
... sec A = 1 ; } ( 1 ) ( c ) tan A 1 1 = cot A = cot A ' or , tan A cot A = 1 . tan A B. The tangent and cotangent in terms of the sine 16-18 . ] 33 RELATIONS BETWEEN RATIOS . Relations between the trigonometric ratios of an acute angle.
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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'.