Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
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Página 24
... similar triangles are con- sidered in Bk . VI . Pupils who study Euclid and have not reached Bk . VI . can be helped to understand these properties by means of a few exercises like those referred to in Ex . 3 , Art . 12 . MP sin RAL ...
... similar triangles are con- sidered in Bk . VI . Pupils who study Euclid and have not reached Bk . VI . can be helped to understand these properties by means of a few exercises like those referred to in Ex . 3 , Art . 12 . MP sin RAL ...
Página 25
... similar manner the other ratios can be shown to be respec- tively unequal . Ex . In this construction AP1 is taken equal to AP . Why does this not affect the generality of the proof ? ( 3 ) This property follows as a corollary from ( 1 ) ...
... similar manner the other ratios can be shown to be respec- tively unequal . Ex . In this construction AP1 is taken equal to AP . Why does this not affect the generality of the proof ? ( 3 ) This property follows as a corollary from ( 1 ) ...
Página 55
... similar to that derived above . Also , derive them . 32. Solution of isosceles triangles . In an isosceles triangle , the perpendicular let fall from the vertex to the base bisects the base and bisects the vertical angle . An isosceles ...
... similar to that derived above . Also , derive them . 32. Solution of isosceles triangles . In an isosceles triangle , the perpendicular let fall from the vertex to the base bisects the base and bisects the vertical angle . An isosceles ...
Página 56
... similar constructions , the solution of the other problems referred to above will be apparent . The perpendicular from the centre of the circle to a side of the inscribed polygon is called the apothem of the polygon . EXAMPLES . 1. The ...
... similar constructions , the solution of the other problems referred to above will be apparent . The perpendicular from the centre of the circle to a side of the inscribed polygon is called the apothem of the polygon . EXAMPLES . 1. The ...
Página 87
... similar to that made in the preceding article . - To deduce sin ( A B ) and cos ( AB ) . Let A and B be two angles each of which is less than a right angle , and let A be the greater . Let the turning line revolve from the initial line ...
... similar to that made in the preceding article . - To deduce sin ( A B ) and cos ( AB ) . Let A and B be two angles each of which is less than a right angle , and let A be the greater . Let the turning line revolve from the initial line ...
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Términos y frases comunes
A+B+C acute angle algebraic angle of elevation central angle CHAPTER circle circumscribing cologarithm column computation cos² cosec cotangent deduced denoted Derive draw equal equation EXAMPLES expression figures find log Find the angle Find the distance Find the height find the number formulas geometrical Given log graph Hence Hipparchus hypotenuse inverse trigonometric functions isosceles triangle law of sines length M₁ mantissa mantissa of log mathematics method negative NOTE number of degrees number of sides OP₁ perpendicular proj Prove radian measure radius regular polygon revolving right angles right-angled triangle sec² secant Show shown sin² sin³ sine and cosine Solve spherical trigonometry subtended tan-¹ tan² tangent terminal line theorems tower triangle ABC trigono trigonometric functions trigonometric ratios turning line whole number X₁
Pasajes populares
Página 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.
Página 54 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.
Página 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Página vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.
Página 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.
Página 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Página 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Página 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.