Trigonometry for BeginnersMacmillan, 1896 - 210 páginas |
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Página 6
... radian is an angle at the centre of a circle , subtended by an arc equal in length to the radius of the circle . Thus if in the circle RPS , whose centre is O , arc ... radian is a then , angle ROP is a radian . 6 TRIGONOMETRY FOR BEGINNERS.
... radian is an angle at the centre of a circle , subtended by an arc equal in length to the radius of the circle . Thus if in the circle RPS , whose centre is O , arc ... radian is a then , angle ROP is a radian . 6 TRIGONOMETRY FOR BEGINNERS.
Página 7
... radian possesses the qualification most essential in a unit ; viz . it is always the same . 18. The reasons why a radian is used as a unit are : ( i . ) All radians are equal to one another . ( ii . ) Its use simplifies many formulæ in ...
... radian possesses the qualification most essential in a unit ; viz . it is always the same . 18. The reasons why a radian is used as a unit are : ( i . ) All radians are equal to one another . ( ii . ) Its use simplifies many formulæ in ...
Página 8
... radians , just as 66099 is used to indicate degrees . Thus is read " radians , " just as 4 ° is read " A degrees . " When the measure of an angle is expressed as some multiple of , e.g. , the unit being the radian , common usage has ...
... radians , just as 66099 is used to indicate degrees . Thus is read " radians , " just as 4 ° is read " A degrees . " When the measure of an angle is expressed as some multiple of , e.g. , the unit being the radian , common usage has ...
Página 9
... radian = arc RP arc RS = arc RP the 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 O R FIG . 6 ...
... radian = arc RP arc RS = arc RP the 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 O R FIG . 6 ...
Página 10
... radians , = X 100 187 180 ° π = X = 105.8 ° nearly . 100 π 25 . EXAMPLES . IV . ( IN THE ANSWERS 22 IS USED for π . ) 1. Find the number of radians in an angle at the centre of a circle of radius 25 feet , which stands on an arc of 371 ...
... radians , = X 100 187 180 ° π = X = 105.8 ° nearly . 100 π 25 . EXAMPLES . IV . ( IN THE ANSWERS 22 IS USED for π . ) 1. Find the number of radians in an angle at the centre of a circle of radius 25 feet , which stands on an arc of 371 ...
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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.