Trigonometry for BeginnersMacmillan, 1896 - 147 páginas |
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Página 11
... difference of two angles is , and their sum 56 ° ; find them . 21. Find the number of radians in an angle of n ' . 22. Express in right angles and in radians the angles ( i . ) of a regular hexagon , ( ii ) of a regular octagon , ( iii ...
... difference of two angles is , and their sum 56 ° ; find them . 21. Find the number of radians in an angle of n ' . 22. Express in right angles and in radians the angles ( i . ) of a regular hexagon , ( ii ) of a regular octagon , ( iii ...
Página 41
... difference between 180 ° and XOP2 may be . If this difference be very small , then XOP , differs from 0 ° by a very small quantity . whence Hence sin XOP1 = 0 , cos XOP1 = 1 , tan XOP1 = 0 ; sin XOP20 , cos XOP - 1 , tan XOP2 = 0 ; or ...
... difference between 180 ° and XOP2 may be . If this difference be very small , then XOP , differs from 0 ° by a very small quantity . whence Hence sin XOP1 = 0 , cos XOP1 = 1 , tan XOP1 = 0 ; sin XOP20 , cos XOP - 1 , tan XOP2 = 0 ; or ...
Página 60
... difference . ( 2 ) The difference of the sines of two angles equals twice the cosine of half their sum multiplied by the sine of half their difference . ( 3 ) The sum of the cosines of two angles equals twice the cosine of half their ...
... difference . ( 2 ) The difference of the sines of two angles equals twice the cosine of half their sum multiplied by the sine of half their difference . ( 3 ) The sum of the cosines of two angles equals twice the cosine of half their ...
Página 61
... difference of two trigonometrical ratios the ten following expressions : 1. 2 sin cos p . • 30 6. 2 cos 2 • COS- 2 7. sin 40 • sin 0 . 2. 2 cos acos B. 3. 2 sin 2 a . cos 3 ß . 4. 2 cos ( a + B ) . cos ( a - ẞ ) . 5. 2 sin 30. cos 5 0 ...
... difference of two trigonometrical ratios the ten following expressions : 1. 2 sin cos p . • 30 6. 2 cos 2 • COS- 2 7. sin 40 • sin 0 . 2. 2 cos acos B. 3. 2 sin 2 a . cos 3 ß . 4. 2 cos ( a + B ) . cos ( a - ẞ ) . 5. 2 sin 30. cos 5 0 ...
Página 86
... difference between the given value and the exact value of the number ) is less than a millionth part of the number . EXAMPLE . 3.141592 is the value of correct to seven significant figures . The error is less than .000001 ; for π is ...
... difference between the given value and the exact value of the number ) is less than a millionth part of the number . EXAMPLE . 3.141592 is the value of correct to seven significant figures . The error is less than .000001 ; for π is ...
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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.