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Page vii
Sidney Luxton Loney. CONTENTS . PART I. CHAP . I. Measurement of angles . Sexagesimal and Centesimal Measure • Circular , or Radian , Measure . II . Trigonometrical Ratios for angles less than a right angle Values for angles of 45 ° , 30 ...
Sidney Luxton Loney. CONTENTS . PART I. CHAP . I. Measurement of angles . Sexagesimal and Centesimal Measure • Circular , or Radian , Measure . II . Trigonometrical Ratios for angles less than a right angle Values for angles of 45 ° , 30 ...
Page x
... right angles = 180 ° 113 7 ( Art . 16. ) = 200o = π radians . ( Art . 19. ) ( Art . 21. ) arc Angle × Radian . radius II . sin2 0 + cos2 0 = 1 ; sec2 = 1 + tan2 0 cosec2 = 1 + cot2 0 . ( Art . 27. ) III . sin 0 ° = 0 ; cos 0 ° = 1 ...
... right angles = 180 ° 113 7 ( Art . 16. ) = 200o = π radians . ( Art . 19. ) ( Art . 21. ) arc Angle × Radian . radius II . sin2 0 + cos2 0 = 1 ; sec2 = 1 + tan2 0 cosec2 = 1 + cot2 0 . ( Art . 27. ) III . sin 0 ° = 0 ; cos 0 ° = 1 ...
Page 1
... angles are measured in terms of a right angle . This , however , is an inconvenient unit of measurement on account of its size . 2. In the Sexagesimal system of measurement a right angle is divided into 90 equal parts called Degrees ...
... angles are measured in terms of a right angle . This , however , is an inconvenient unit of measurement on account of its size . 2. In the Sexagesimal system of measurement a right angle is divided into 90 equal parts called Degrees ...
Page 2
... right angle is divided into 100 equal parts , called Grades ; each grade is subdivided into 100 Minutes , and each minute into 100 Seconds . The symbols 18 , 1 ' , and 1 " are used to denote a Grade , a Minute , and a Second ...
... right angle is divided into 100 equal parts , called Grades ; each grade is subdivided into 100 Minutes , and each minute into 100 Seconds . The symbols 18 , 1 ' , and 1 " are used to denote a Grade , a Minute , and a Second ...
Page 3
... angle . The method will be seen in the following examples ; Ex . 1. Reduce 63 ° 14 ' 51 " to Centesimal Measure . We ... right angle 90 84.81483 degrees 60 48.8898 minutes 60 53.3880 seconds .. 948 23 ' 87 " 84 ° 48 ′ 53.388 " . 6 ...
... angle . The method will be seen in the following examples ; Ex . 1. Reduce 63 ° 14 ' 51 " to Centesimal Measure . We ... right angle 90 84.81483 degrees 60 48.8898 minutes 60 53.3880 seconds .. 948 23 ' 87 " 84 ° 48 ′ 53.388 " . 6 ...
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a+b+c a+ẞi A₁ ad inf angle AOP angle of elevation Binomial Theorem centre circle circumcircle coefficient complex quantity cosı cos² cos³ cosec cosh cosine cotangent denoted Diff distance equal EXAMPLES expression feet Find the angle find the height find the values flagstaff given log Hence infinite inscribed integer last article length loga logarithm loge miles multiple nearly number of radians pedal triangle perpendicular places of decimals principal value prove quadrant quadrilateral r₁ radius regular polygon revolving line right angle sec² secant shew shewn sides Similarly sin sin sin sinı sin² sin³ sine sinh tan-ı tan² tan³ tangent tanh Theorem tower triangle ABC trigonometrical functions trigonometrical ratios unity x+yi zero α α π π
Popular passages
Page 36 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 17 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 44 - A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 50°; walking 40 ft.
Page 13 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef.
Page 1 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 10 - If the radius of the earth be 4000 miles, what is the length of its circumference?
Page 42 - From the top of a cliff 150 ft. high the angles of depression of the top and bottom of a tower are 30° and 60°, respectively.
Page 220 - A ladder placed at an angle of 75° just reaches the sill of a window at a height of 27 feet above the ground on one side of a street. On turning the ladder over without moving its foot, it is found that when it rests against a wall on the other side of the street it is at an angle of 15° with the ground.
Page 215 - From the top of a hill the angles of depression of two objects situated in the...