Plane TrigonometryLongmans, Green, and Company, 1906 |
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Página xi
... formulas for all values of the two angles • 85 87 49. Each fundamental formula contains the others 50. Ratios of an angle in terms of the ratios of its half angle · 51. Tangents of the sum and difference of two angles , and of twice an ...
... formulas for all values of the two angles • 85 87 49. Each fundamental formula contains the others 50. Ratios of an angle in terms of the ratios of its half angle · 51. Tangents of the sum and difference of two angles , and of twice an ...
Página 42
... also be wrong . Hence it is advisable to check the values found by seeing whether they satisfy relations differing from those already employed . For example , check formulas which may be used in 42 [ CH . IIL PLANE TRIGONOMETRY .
... also be wrong . Hence it is advisable to check the values found by seeing whether they satisfy relations differing from those already employed . For example , check formulas which may be used in 42 [ CH . IIL PLANE TRIGONOMETRY .
Página 43
... formulas is necessary in cases in which the answers are not given . The test- ing of the results also affords practice in the use of formulas and in computation . When a check formula is satisfied it is highly probable , but not ...
... formulas is necessary in cases in which the answers are not given . The test- ing of the results also affords practice in the use of formulas and in computation . When a check formula is satisfied it is highly probable , but not ...
Página 44
... Formulas tan A = a b ( 1 ) b Checks : tan B B = 90 ° - A. ( 2 ) α α C = ( 3 ) sin A a2 = c2 - b2 = ( c + b ) ( cb ) . * This is to be filled after the values of the unknown quantities have been found . It is advisable to indicate the ...
... Formulas tan A = a b ( 1 ) b Checks : tan B B = 90 ° - A. ( 2 ) α α C = ( 3 ) sin A a2 = c2 - b2 = ( c + b ) ( cb ) . * This is to be filled after the values of the unknown quantities have been found . It is advisable to indicate the ...
Página 45
... formula tan B b = - α can be used instead of ( 2 ) . A check then is A + B = 90 ° . Instead of ( 3 ) , one of the following formulas can be used , viz . C = b sin B ' α b c = c = cos B ' cos A There is often a choice of formulas that ...
... formula tan B b = - α can be used instead of ( 2 ) . A check then is A + B = 90 ° . Instead of ( 3 ) , one of the following formulas can be used , viz . C = b sin B ' α b c = c = cos B ' cos A There is often a choice of formulas that ...
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Términos y frases comunes
A+B+C acute angle algebraic centre CHAPTER circumscribing computation cos² 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 sin² solid angle solution Solve ABC sphere spherical angle spherical degree spherical excess spherical polygon spherical triangle spherical trigonometry subtended surface tables tan² tangent terminal line three angles tower triangle ABC trigono trigonometric functions trigonometric ratios π π
Pasajes populares
Página 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...
Página 42 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 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...
Página 74 - The area of the surface of a sphere is four times the area of a great circle.
Página 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.
Página 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...
Página 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.
Página 128 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 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.
Página 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