Trigonometry for BeginnersMacmillan, 1896 - 147 páginas |
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Página 13
... cosine of angle A , and is read , cosine A ; OP MP III . , is called the tangent of angle A , and is read , tangent A ; OM OP IV . , is called the cosecant of angle A , and is read , cosecant A ; MP OP V. , is called the secant of angle ...
... cosine of angle A , and is read , cosine A ; OP MP III . , is called the tangent of angle A , and is read , tangent A ; OM OP IV . , is called the cosecant of angle A , and is read , cosecant A ; MP OP V. , is called the secant of angle ...
Página 18
... cosine , and tangent of each acute angle of the triangle . 7. The sides of a right - angled triangle are in the ratio 1 : 2 : √3 ; find the sine , cosine , and tangent of each acute angle of the triangle . 8. Prove that if A be either ...
... cosine , and tangent of each acute angle of the triangle . 7. The sides of a right - angled triangle are in the ratio 1 : 2 : √3 ; find the sine , cosine , and tangent of each acute angle of the triangle . 8. Prove that if A be either ...
Página 19
... cosine , and tangent of an angle of 45 ° . When one angle of a right - angled triangle is 45 ° , that is , the half of a right angle , the third angle must also be 45 ° . Hence 45 ° is one angle of an isosceles right - angled triangle ...
... cosine , and tangent of an angle of 45 ° . When one angle of a right - angled triangle is 45 ° , that is , the half of a right angle , the third angle must also be 45 ° . Hence 45 ° is one angle of an isosceles right - angled triangle ...
Página 20
... cosine , and tangent of an angle of 60 ° . Each angle in an equilateral triangle is 60 ° , because they are each one - third of 180 ° . If we draw a perpendicular from one of the angu- lar points of the triangle to the side opposite ...
... cosine , and tangent of an angle of 60 ° . Each angle in an equilateral triangle is 60 ° , because they are each one - third of 180 ° . If we draw a perpendicular from one of the angu- lar points of the triangle to the side opposite ...
Página 21
... cosine , and tangent of an angle of 30 ° . With the same figure and construction as above we have the angle OPM = 30 ° , since it is half of OPQ , i.e. of 60 ° . 13.m MO m 1 Hence , sin 30 ° = sin OPM : = PO 2m 2 ' PM cos 30 ° = cos OPM ...
... cosine , and tangent of an angle of 30 ° . With the same figure and construction as above we have the angle OPM = 30 ° , since it is half of OPQ , i.e. of 60 ° . 13.m MO m 1 Hence , sin 30 ° = sin OPM : = PO 2m 2 ' PM cos 30 ° = cos OPM ...
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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.