Elementary Text-book of TrigonometryBlackie & Son, 1884 - 176 páginas |
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Página 25
... opposite side AC ; then the triangle ABD is a right - angled triangle in which the angle BAD is 60 ° and the angle ABD is 30 ° . Let a denote the length of the side AD , which is half of AC or AB , then the length of AB is denoted by 2a ...
... opposite side AC ; then the triangle ABD is a right - angled triangle in which the angle BAD is 60 ° and the angle ABD is 30 ° . Let a denote the length of the side AD , which is half of AC or AB , then the length of AB is denoted by 2a ...
Página 43
... opposite these angles . In the triangle we are considering C = 90 ° , and therefore by the definitions a b = tanA or cotB ; therefore α = b tanA or b cotB . α -sinA or cosB ; с ac sinA or c cosB . Again therefore Hence we can express ...
... opposite these angles . In the triangle we are considering C = 90 ° , and therefore by the definitions a b = tanA or cotB ; therefore α = b tanA or b cotB . α -sinA or cosB ; с ac sinA or c cosB . Again therefore Hence we can express ...
Página 47
... opposite , is 25 ° 37 ′ ; find the height of the tree , given tan25 ° 37 ′ = ' 479 . Here therefore CA = 100 feet , tan ACB = tan 25 ° 37 ' = ' 479 ; AB , the height of the tree = 100 × 479 = 47.9 feet . Ex . 3. From the top of a cliff ...
... opposite , is 25 ° 37 ′ ; find the height of the tree , given tan25 ° 37 ′ = ' 479 . Here therefore CA = 100 feet , tan ACB = tan 25 ° 37 ' = ' 479 ; AB , the height of the tree = 100 × 479 = 47.9 feet . Ex . 3. From the top of a cliff ...
Página 58
... opposite to that of the hands of a watch . But angles may , of course , be described by a line revolving in the same ... opposite direction negative quantities . It is usual in all branches of mathematics to con- sider the direction ...
... opposite to that of the hands of a watch . But angles may , of course , be described by a line revolving in the same ... opposite direction negative quantities . It is usual in all branches of mathematics to con- sider the direction ...
Página 68
... opposite directions . If OP and OP ' are taken equal along OC and OC , PP ' will be perpendicular to OA , and A the two triangles POM and P'OM will be equal in all respects . Hence the ratios of the angle + A and of the angle A will be ...
... opposite directions . If OP and OP ' are taken equal along OC and OC , PP ' will be perpendicular to OA , and A the two triangles POM and P'OM will be equal in all respects . Hence the ratios of the angle + A and of the angle A will be ...
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Términos y frases comunes
angle AOB angle BAC angle increases angle less Article base centre circumference cloth boards common logarithm complement cos(A+B cos2A cos4A cosB cosC cose cosecA cosine cotA cotangent decimal places degree measure diameter distance equal equation Euclid EXAMPLES feet Find the angle Find the height find the number find the values flagstaff following angles formula given Hence hypotenuse inches log2 loga logarithms of numbers magnitude mantissa miles negative numbers number expressing number of degrees numerical value perpendicular positive Prove quadrant radian measure radii ratios of angles regular polygon respectively right angle right-angled triangle sec²A secA secant side BC Similarly sin(A sin(A+B sin2A sin2B sin3A sinB sine sine and cosine square root table of logarithms tan(A+B tan²A tanA tanB tangent tanß tower triangle ABC trigono trigonometrical ratios unit of angle yards
Pasajes populares
Página 90 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm, m — ax, and n = a".
Página 90 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Página 118 - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Página 149 - Find the length of the side of a square whose area is equal to that of a rectangle the sides of which are 94 '28 and 6720 yards.
Página 89 - The logarithm of a number is the index of the power to which the base of the system must be raised to equal a given number.
Página 158 - The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5.