Trigonometry for BeginnersMacmillan, 1896 - 147 páginas |
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Página 29
... , the negative sense is determined . ( 2 ) That the line is the result of the movement , not the P process . RADIUS VECTOR INITIAL LINE -X ORIGIN FIG . 23 . 51. We have already said in Art . 5 ( THE TRIGONOMETRIC RATIOS 29.
... , the negative sense is determined . ( 2 ) That the line is the result of the movement , not the P process . RADIUS VECTOR INITIAL LINE -X ORIGIN FIG . 23 . 51. We have already said in Art . 5 ( THE TRIGONOMETRIC RATIOS 29.
Página 48
... determined . If , however , we know tan 0 and in addition to what quadrant belongs , we can determine the respective signs . of the ratios named . E.g. if tan√3 and we know that is of the third quadrant , then sin √3 = - EXAMPLES . XV ...
... determined . If , however , we know tan 0 and in addition to what quadrant belongs , we can determine the respective signs . of the ratios named . E.g. if tan√3 and we know that is of the third quadrant , then sin √3 = - EXAMPLES . XV ...
Página 64
... determined . The converse is not true ; i.e. if cos 2 A is given , sin A and cos A have a sign ambiguity . We have cos2 A = cos 2 A +1 2 • ... cos A cos 2 A +1 = ± 2 1 Similarly , sin A cos 2 A = ± ; 2 2 cos 2 If sin 2 A be given , we ...
... determined . The converse is not true ; i.e. if cos 2 A is given , sin A and cos A have a sign ambiguity . We have cos2 A = cos 2 A +1 2 • ... cos A cos 2 A +1 = ± 2 1 Similarly , sin A cos 2 A = ± ; 2 2 cos 2 If sin 2 A be given , we ...
Página 93
... determined when there are given : I. Three sides . II . One side and two angles . III . Two sides and the included angle . And IV . That either one , two , or no triangles are determined when two sides and the angle opposite one of them ...
... determined when there are given : I. Three sides . II . One side and two angles . III . Two sides and the included angle . And IV . That either one , two , or no triangles are determined when two sides and the angle opposite one of them ...
Página 95
... determine b and c . 148. In practical work we proceed as follows : Since b = a . sin B sin A a . sin B sin A .. log blog log a + log sin B – log sin A ... determined . And B and C can be found when the values THE SOLUTION OF TRIANGLES 95.
... determine b and c . 148. In practical work we proceed as follows : Since b = a . sin B sin A a . sin B sin A .. log blog log a + log sin B – log sin A ... determined . And B and C can be found when the values THE SOLUTION OF TRIANGLES 95.
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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.