Plane Trigonometry |
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Page 7
... Hence we have Perimeter of the outer polygon_n . AB .AB AB OA Perimeter of the inner polygon n.ab ab Оа • .. ( 1 ) . This relation exists whatever be the number of sides in the polygons . Let then the number of sides be indefinitely ...
... Hence we have Perimeter of the outer polygon_n . AB .AB AB OA Perimeter of the inner polygon n.ab ab Оа • .. ( 1 ) . This relation exists whatever be the number of sides in the polygons . Let then the number of sides be indefinitely ...
Page 8
... Hence Circumference Diameter the constant number π . We have therefore the following theorem ; The cir- cumference of a circle is always equal to π times its diameter or 27 times its radius . 13. Unfortunately the value of T is not a ...
... Hence Circumference Diameter the constant number π . We have therefore the following theorem ; The cir- cumference of a circle is always equal to π times its diameter or 27 times its radius . 13. Unfortunately the value of T is not a ...
Page 11
Sidney Luxton Loney. 2 Hence a Radian ZAOB IE NIE 2 π × a right angle . Since a right angle is a constant angle and since ... Hence when the revolving line ( Art . 6 ) has made a complete revolution it has described an angle equal to 2π ...
Sidney Luxton Loney. 2 Hence a Radian ZAOB IE NIE 2 π × a right angle . Since a right angle is a constant angle and since ... Hence when the revolving line ( Art . 6 ) has made a complete revolution it has described an angle equal to 2π ...
Page 15
... Hence the theorem is proved . 22 . Ex . 1. Find the angle subtended at the centre of a circle of radius 3 feet by an arc of length 1 foot . arc 1 The number of radians in the angle radius 3 Hence the angle 1 1 2 2 60 ° radian right ...
... Hence the theorem is proved . 22 . Ex . 1. Find the angle subtended at the centre of a circle of radius 3 feet by an arc of length 1 foot . arc 1 The number of radians in the angle radius 3 Hence the angle 1 1 2 2 60 ° radian right ...
Page 16
... Hence , by Art . 21 , we have D 92500000 the number of radians in 32 ' 8 ° the number of radians in 15 8 π 2π X 15 180 675 185000000 . D = π miles 675 185000000 22 X 675 7 miles approximately = about 862000 miles . Ex . 4. Assuming that ...
... Hence , by Art . 21 , we have D 92500000 the number of radians in 32 ' 8 ° the number of radians in 15 8 π 2π X 15 180 675 185000000 . D = π miles 675 185000000 22 X 675 7 miles approximately = about 862000 miles . Ex . 4. Assuming that ...
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Common terms and phrases
a+b+c a+ẞi A₁ ad inf angle AOP angle of elevation Binomial Theorem centre circle circumcircle coefficient complex quantity cos¹ 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 sin¹ sin² sin³ sine sinh tan-¹ 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...