Trigonometry for BeginnersMacmillan, 1896 - 147 páginas |
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Página 11
... Show that the measure of the angle at the centre of a circle of radius r , k · α which stands on an arc a , is where k depends solely on the unit of angle r employed . Find when the unit is ( i . ) a radian , ( ii . ) a degree . 20. The ...
... Show that the measure of the angle at the centre of a circle of radius r , k · α which stands on an arc a , is where k depends solely on the unit of angle r employed . Find when the unit is ( i . ) a radian , ( ii . ) a degree . 20. The ...
Página 15
... show I. That so long as1 the angle remains unchanged , the ratios remain unchanged . II . That a small change in the angle produces a change in each of the ratios . M " E M ' P M FIG . 12 . P ' R p " I. Take any angle ROE ; let P be any ...
... show I. That so long as1 the angle remains unchanged , the ratios remain unchanged . II . That a small change in the angle produces a change in each of the ratios . M " E M ' P M FIG . 12 . P ' R p " I. Take any angle ROE ; let P be any ...
Página 17
... , and we let A , B , and C stand for the angles at A , B , and C respectively , and let a , b , and c be the measures of the sides opposite the angles A , B , and C respectively : C Show that sin A = a , cos A b THE ACUTE ANGLE 17.
... , and we let A , B , and C stand for the angles at A , B , and C respectively , and let a , b , and c be the measures of the sides opposite the angles A , B , and C respectively : C Show that sin A = a , cos A b THE ACUTE ANGLE 17.
Página 18
John Bascombe Lock John Anthony Miller. Show that sin A = a , cos A b = с с tan A = Show also that sin2 A + cos2 A = 1 . α ( ii . ) b = c . sin B , Show also that ( i . ) a = c . sin A , ( iv . ) b = ccos A , ( v . ) sin A = = cos B ...
John Bascombe Lock John Anthony Miller. Show that sin A = a , cos A b = с с tan A = Show also that sin2 A + cos2 A = 1 . α ( ii . ) b = c . sin B , Show also that ( i . ) a = c . sin A , ( iv . ) b = ccos A , ( v . ) sin A = = cos B ...
Página 32
... show that the trigonometrical ratios of an angle vary in Sign according to the Quadrant in which the radius . vector of the angle happens to be . From the definition we have , with the usual letters , sin XOP = = MP OP ' cos XOP = = OM ...
... show that the trigonometrical ratios of an angle vary in Sign according to the Quadrant in which the radius . vector of the angle happens to be . From the definition we have , with the usual letters , sin XOP = = MP OP ' cos XOP = = OM ...
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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.