Plane TrigonometryLongmans, Green, and Company, 1906 |
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Page 55
... 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 triangle can often be solved on ...
... 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 triangle can often be solved on ...
Page 88
... B ) and sin ( A — B ) were given by Pitiscus ( 1561-1613 ) , a German mathematician and astronomer , in his Trig- onometry published in 1595 . 1 EXAMPLES . 1. Derive sin 15 ° , cos 88 [ CH . VI . PLANE TRIGONOMETRY .
... B ) and sin ( A — B ) were given by Pitiscus ( 1561-1613 ) , a German mathematician and astronomer , in his Trig- onometry published in 1595 . 1 EXAMPLES . 1. Derive sin 15 ° , cos 88 [ CH . VI . PLANE TRIGONOMETRY .
Page 89
Daniel Alexander Murray. 1 EXAMPLES . 1. Derive sin 15 ° , cos 15 ° , on putting 60 ° 45 ° for 15 ° . 2. Derive sin 15 ° , cos 15 ° , on putting 45 ° 30 ° for 15 ° . 3. Find sin ( x - y ) , cos ( x − y ) in the cases in Ex . 8 , Art ...
Daniel Alexander Murray. 1 EXAMPLES . 1. Derive sin 15 ° , cos 15 ° , on putting 60 ° 45 ° for 15 ° . 2. Derive sin 15 ° , cos 15 ° , on putting 45 ° 30 ° for 15 ° . 3. Find sin ( x - y ) , cos ( x − y ) in the cases in Ex . 8 , Art ...
Page 90
... derive the other three fundamental formulas . Ex . 2. So also , from formula ( 3 ) , Art . 47 . Ex . 3. So also , from formula ( 4 ) , Art . 47 . 50. Ratio of an angle in terms of the ratios of its half angle . In this article and Arts ...
... derive the other three fundamental formulas . Ex . 2. So also , from formula ( 3 ) , Art . 47 . Ex . 3. So also , from formula ( 4 ) , Art . 47 . 50. Ratio of an angle in terms of the ratios of its half angle . In this article and Arts ...
Page 93
... Derive cot ( A + B ) = cot A cot BF1 cot Bcot A cot2 A - 1 cot 2 A = - 2 cot A 52. Sums and differences of sines and cosines . The set of formulas ( 1 ) - ( 4 ) , Art . 50 , can be transformed into two other sets which are very useful ...
... Derive cot ( A + B ) = cot A cot BF1 cot Bcot A cot2 A - 1 cot 2 A = - 2 cot A 52. Sums and differences of sines and cosines . The set of formulas ( 1 ) - ( 4 ) , Art . 50 , can be transformed into two other sets which are very useful ...
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A+B+C acute angle algebraic centre CHAPTER circumscribing computation cosē cosec cotangent deduced denoted Derive diedral angle draw equal equator EXAMPLES expression figure Find the distance formulas geometry given Hence hypotenuse included angle inscribed circle intersection latitude law of cosines law of sines length logarithms mantissa mathematics meridian method NOTE number of degrees number of sides opposite perpendicular plane triangle Plane Trigonometry polar triangle pole positive quadrant radian measure radii radius regular polygon relations respectively right angles right triangles right-angled triangle secant Show sides and angles sinē solid angle solution Solve ABC sphere spherical angle spherical degree spherical excess spherical polygon spherical triangle spherical trigonometry subtended surface tables tanē tangent terminal line three angles tower triangle ABC trigono trigonometric functions trigonometric ratios π π
Popular passages
Page 52 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Page 42 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 108 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 74 - The area of the surface of a sphere is four times the area of a great circle.
Page 108 - 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 and the cosine of their included angle.
Page 72 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 62 - Geometry that 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 THE RIGHT TRIANGLE.
Page 128 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 200 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Page 202 - Find the area of a regular polygon of n sides inscribed in a circle, and show, by increasing the number of sides of the polygon without limit, how the expression for the area of the circle may be obtained. 13. (a) Find the distance at which a building 50 ft. wide will subtend an angle of 3'. (6) A church spire 45 ft. high subtends an angle of 9