Trigonometry for BeginnersMacmillan, 1896 - 147 páginas |
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Página 3
... radius vector . When referring to the angle XOP the lines OX and OP are called the sides of the angle , and O is called its vertex . 7. To add angle X'OP ' to angle XOP , both being positive , revolve OP from its final position when it ...
... radius vector . When referring to the angle XOP the lines OX and OP are called the sides of the angle , and O is called its vertex . 7. To add angle X'OP ' to angle XOP , both being positive , revolve OP from its final position when it ...
Página 6
... radius of the circle . Thus if in the circle RPS , whose centre is 0 , arc RP radius OR , = 16. We shall now prove that the radian is a then , angle ROP is a radian . 6 TRIGONOMETRY FOR BEGINNERS.
... radius of the circle . Thus if in the circle RPS , whose centre is 0 , arc RP radius OR , = 16. We shall now prove that the radian is a then , angle ROP is a radian . 6 TRIGONOMETRY FOR BEGINNERS.
Página 7
... radius , then the angles at the centres of these circles which stand on these arcs respectively , will be all of the same size . FIG . 5 . R 17. To prove that all radians are equal to one another . Since the radian at the centre of a ...
... radius , then the angles at the centres of these circles which stand on these arcs respectively , will be all of the same size . FIG . 5 . R 17. To prove that all radians are equal to one another . Since the radian at the centre of a ...
Página 9
... radius Hence the angle ROP = arc RP radians . the radius So that the circular measure of an angle ( at the centre of a circle ) is the ratio of its arc to the radius . S L P RADIUS RADIAN R FIG . 6 . MEASUREMENT OF ANGLES 9.
... radius Hence the angle ROP = arc RP radians . the radius So that the circular measure of an angle ( at the centre of a circle ) is the ratio of its arc to the radius . S L P RADIUS RADIAN R FIG . 6 . MEASUREMENT OF ANGLES 9.
Página 10
... radius is 25 feet . The angle stands on an arc of 463 feet , and the radian , at the centre of the same circle ... radius 25 feet , which stands on an arc of 37 feet . 2. Find the number of degrees in an angle at the centre of a circle ...
... radius is 25 feet . The angle stands on an arc of 463 feet , and the radian , at the centre of the same circle ... radius 25 feet , which stands on an arc of 37 feet . 2. Find the number of degrees in an angle at the centre of a circle ...
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Términos y frases comunes
angle of elevation angle XOP Asin Atan centre circle circular measure circumference common logarithms cos² cosec cosine cot² cotangent decimal diameter difference distance equal equation EXAMPLE Express find log find the angles find the height find the logarithm Find the number find the sine following angles formulæ fraction Geom geometrical given greatest angle Hence inverse trigonometric functions length less than 90 Let XOP log cot log log tan log magnitude mantissa miles negative number of degrees number whose logarithm observed perpendicular plane positive quadrant radians respectively right angles right triangle right-angled triangle sec² sin B sin sin² sin³ Solve the triangle spherical triangle student subtended tan log sin tan² tangent tower triangle ABC trigonometric functions trigonometrical ratios XOP₁ yards ΙΟ ΙΟΙ
Pasajes populares
Página 85 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant figure.
Página 6 - A radian is an angle at the center of a circle, subtended by an arc equal in length to the radius of the circle.
Página 85 - The characteristic of the logarithm of a number greater than unity is one less than the number of figures in the integral part of the number.
Página 118 - To prove that sin (A - B) = sin A cos B - cos A sin B, and cos (A — £) = cos A cos B + sin A sin B.
Página 25 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Página 126 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 117 - Express in degrees, minutes, etc., (i.) the angle whose circular measure is ^V7'"! (".) t^e angle whose circular measure is 5. If the angle subtended at the centre of a circle by the side of a regular pentagon be the unit of angular measurement, by what number is a right angle represented ? 2. Find, by geometrical constructions, the cosine of 45° and the sine of 120°. Prove that (sin 30° + cos 30°) (sin 120° + cos 120°) = sin 30°. 3. If esc A = 9, find cot A and sec A. 4. Prove that cos (180°...
Página 107 - The elevation of a steeple at a place due south of it is 45°, and at another place due west of it the elevation is 15°. If the distance between the two places be a, prove that the height of the steeple is a( \/3 — 1) -^2\/3.
Página vii - ... are not as many figures in the quotient as there are ciphers annexed to the dividend. In such a case, supply the deficiency, as in the division of decimals, by prefixing a cipher or ciphers to the quotient before annexing.