Trigonometry for BeginnersMacmillan, 1896 - 210 páginas |
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Página 3
... represents angle XOP , P FIG . 4 . P X through an angle equal to angle X'OP ' ; call this position OP1⁄2 Then , Z XOP1 = 4 XOP + X'OP ' . EXAMPLES . I. Give a geometrical representation of each of the following angles , the initial line ...
... represents angle XOP , P FIG . 4 . P X through an angle equal to angle X'OP ' ; call this position OP1⁄2 Then , Z XOP1 = 4 XOP + X'OP ' . EXAMPLES . I. Give a geometrical representation of each of the following angles , the initial line ...
Página 4
... represents it exactly , so that we have no numerical expression whatever , arithmetical nor algebraical , to represent exactly the ratio of the circumference of a circle to its diameter . Hence the universal custom has arisen , of ...
... represents it exactly , so that we have no numerical expression whatever , arithmetical nor algebraical , to represent exactly the ratio of the circumference of a circle to its diameter . Hence the universal custom has arisen , of ...
Página 28
... represented by + b , where b is its measure , then a line segment generated by movement in the opposite direction is represented by b , if b be its measure . Thus line segments generated in opposite senses furnish an illus- tration of ...
... represented by + b , where b is its measure , then a line segment generated by movement in the opposite direction is represented by b , if b be its measure . Thus line segments generated in opposite senses furnish an illus- tration of ...
Página 29
... represented algebraically by their measures with the sign + before them ; then Lines drawn parallel to OX in the opposite sense are negative ; that is , are represented algebraically by their measures with the sign - before them . - 49 ...
... represented algebraically by their measures with the sign + before them ; then Lines drawn parallel to OX in the opposite sense are negative ; that is , are represented algebraically by their measures with the sign - before them . - 49 ...
Página 30
... represented algebraically by its measure with the sign + before it . ( ii . ) that , when an angle XOP is described by OP turning about O in the same direction as the hands of a watch , the angle is said to be negative ; that is , is ...
... represented algebraically by its measure with the sign + before it . ( ii . ) that , when an angle XOP is described by OP turning about O in the same direction as the hands of a watch , the angle is said to be negative ; that is , is ...
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Términos y frases comunes
A+ cos² angle of elevation angle XOP Asin Atan centre circle circular measure circumference cos² cosec cosine cot log cos 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 greater Hence inverse trigonometric functions length less than 90 log cot log log tan log magnitude mantissa miles negative number of degrees number whose logarithm perpendicular plane positive quadrant radians radius respectively right angles right-angled triangle sec² Show significant figures sin b sin sin² sin³ Solve the triangle spherical triangle spire student subtended tan log sin tan² tangent tower triangle ABC trigonometrical ratios XOP₁ yards ΙΟ ΙΟΙ π π
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 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 122 - 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 82 - Whence x + y is the logarithm of mn. q. BD 10. Prop. 2. — Tlie logarithm of the quotient of two numbers is the logarithm, of the dividend minus the logarithm of the divisor.
Página iii - ... 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.
Página 135 - Two solutions exist so long as both values of c are positive, and less than 180°, that is, so long as sin c is positive. Now when a differs more from 90° than b, we have (neglecting the signs for a moment), cos a > cos...
Página 115 - Express in degrees, minutes, etc., (i.) the angle whose circular measure is -^tr; (ii.) the 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.
Página 82 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 113 - A° in circular measure. 2. Define the sine, secant, and cotangent of an angle, and express any two of these ratios in terms of the third. Find the trigonometrical ratios of the angle whose cosine isf.