Trigonometry for BeginnersMacmillan, 1896 - 210 páginas |
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Página 13
... tangent of angle A , and is read , tangent A ; OM OP MP is called the cosecant of angle A , and is read , cosecant A ; OP V. , is called the secant of angle A , and is read , secant A ; OM VI . is called the cotangent of A , and is read ...
... tangent of angle A , and is read , tangent A ; OM OP MP is called the cosecant of angle A , and is read , cosecant A ; OP V. , is called the secant of angle A , and is read , secant A ; OM VI . is called the cotangent of A , and is read ...
Página 18
... 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 of the angles ...
... 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 of the angles ...
Página 19
... 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 . P √2m x ...
... 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 . P √2m x ...
Página 20
... 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 , we get a right ...
... 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 , we get a right ...
Página 21
... 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 ° . = 2m 13 • m = Hence , sin 30 ° MO = sin OPM : m = = = PO cos 30 ° PM = cos OPM = = PO tan ...
... 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 ° . = 2m 13 • m = Hence , sin 30 ° MO = sin OPM : m = = = PO cos 30 ° PM = cos OPM = = PO tan ...
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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.