Plane Trigonometry |
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Page vii
... and submultiple angles 105 Explanation of ambiguities 117 Angles of 18 ° , 36 ° , and 9 ° 126 IX . Identities and trigonometrical equations . 131 X. Logarithms 146 Tables of logarithms 152 CHAP . XI . Principle of Proportional Parts XII .
... and submultiple angles 105 Explanation of ambiguities 117 Angles of 18 ° , 36 ° , and 9 ° 126 IX . Identities and trigonometrical equations . 131 X. Logarithms 146 Tables of logarithms 152 CHAP . XI . Principle of Proportional Parts XII .
Page ix
... equation Evaluation of indeterminate quantities PAGE 323 328 331 332 334 XXIV . Expansions of cos " and sin " in cosines or sines of multiples of • Expansions of sin ne and cos ne in series of descend- ing and ascending powers of sin ...
... equation Evaluation of indeterminate quantities PAGE 323 328 331 332 334 XXIV . Expansions of cos " and sin " in cosines or sines of multiples of • Expansions of sin ne and cos ne in series of descend- ing and ascending powers of sin ...
Page 22
... equation ( 1 ) by OM2 , we have MP \ 2 +1 OM OM ( OP ) * 2 i.e. so that ( tan 0 ) 2 + 1 = ( sec 0 ) 2 , sec2 = 1 + tan2 0 ... .. Again , dividing equations ( 1 ) by MP2 we have OM \ 2 1+ ( M7 ) 2 = ( OP ) " , MP MP ( 3 ) . i.e. so that ...
... equation ( 1 ) by OM2 , we have MP \ 2 +1 OM OM ( OP ) * 2 i.e. so that ( tan 0 ) 2 + 1 = ( sec 0 ) 2 , sec2 = 1 + tan2 0 ... .. Again , dividing equations ( 1 ) by MP2 we have OM \ 2 1+ ( M7 ) 2 = ( OP ) " , MP MP ( 3 ) . i.e. so that ...
Page 25
... cos2 A = 1 + versin2 A. 29. Limits to the values of the trigonometrical ratios . From equation ( 2 ) of Art . 27 we have sin20 + cos2 0 = 1 . Now sin ' and cos 0 , being both squares [ Exs . V. ] 25 TRIGONOMETRICAL RATIOS .
... cos2 A = 1 + versin2 A. 29. Limits to the values of the trigonometrical ratios . From equation ( 2 ) of Art . 27 we have sin20 + cos2 0 = 1 . Now sin ' and cos 0 , being both squares [ Exs . V. ] 25 TRIGONOMETRICAL RATIOS .
Page 63
... equation 3 cosec2 = 2 sec 0 . 10. A man on a cliff observes a boat at an angle of depression of 30 ° , which is ... equation sin 0 = x + is impossible if x be real . X 12. Shew that the equation sec2 0 = x = y . 4xy is only possible when ...
... equation 3 cosec2 = 2 sec 0 . 10. A man on a cliff observes a boat at an angle of depression of 30 ° , which is ... equation sin 0 = x + is impossible if x be real . X 12. Shew that the equation sec2 0 = x = y . 4xy is only possible when ...
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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...