Trigonometry for BeginnersMacmillan, 1896 - 210 páginas |
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Página 1
... called Angular Analysis . 2. The figures with which we shall be concerned in our study of Trigonometry are , with the exception of the line and the angle , the same as those of Geometry ; i.e. they are subject to the same limi- tations ...
... called Angular Analysis . 2. The figures with which we shall be concerned in our study of Trigonometry are , with the exception of the line and the angle , the same as those of Geometry ; i.e. they are subject to the same limi- tations ...
Página 3
... called the origin . The line OX is the initial line . The line OP is the revolving line or 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 ...
... called the origin . The line OX is the initial line . The line OP is the revolving line or 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 ...
Página 6
... called a degree ; each degree is subdivided into 60 equal parts , each of which is called a minute ; and each minute is again sub- divided into 60 equal parts , each of which is called a second . Instruments used for measuring angles ...
... called a degree ; each degree is subdivided into 60 equal parts , each of which is called a minute ; and each minute is again sub- divided into 60 equal parts , each of which is called a second . Instruments used for measuring angles ...
Página 12
... . These ratios are of much importance in all mathematical investigations . For convenience , they have been given the follow- ing names . If XOP be the angle A , then MP 1 I. , is called the sine of angle 12 THE TRIGONOMETRICAL RATIOS.
... . These ratios are of much importance in all mathematical investigations . For convenience , they have been given the follow- ing names . If XOP be the angle A , then MP 1 I. , is called the sine of angle 12 THE TRIGONOMETRICAL RATIOS.
Página 13
... called the cosine of angle A , and is read , cosine A ; OP IV . , MP III . , is called the tangent of angle A , and is read , tangent A ; OM OP MP is called the cosecant of angle A , and is read , cosecant A ; OP V. , is called the ...
... called the cosine of angle A , and is read , cosine A ; OP IV . , MP III . , is called the tangent of angle A , and is read , tangent A ; OM OP MP is called the cosecant of angle A , and is read , cosecant A ; OP V. , is called the ...
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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.