Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 Seiten |
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Seite 34
... opposite the angle OCR , is equal to OR ' , opposite the equal angle OCR ' . Since OR is esti- mated upward , and OR ' downward , they have contrary signs ; hence , OROR ' . But OR is the tangent of the arc OT , and OR ' is the 34 ...
... opposite the angle OCR , is equal to OR ' , opposite the equal angle OCR ' . Since OR is esti- mated upward , and OR ' downward , they have contrary signs ; hence , OROR ' . But OR is the tangent of the arc OT , and OR ' is the 34 ...
Seite 36
... opposite the angle O'CS , is equal to O'S ' , opposite the equal angle O'CS ' . Since O'S is estimated to the right , and O'S ' to the left , they have contrary signs ; hence , O'S = - O'S ' . But O'S is the co - tangent of OT , and O'S ...
... opposite the angle O'CS , is equal to O'S ' , opposite the equal angle O'CS ' . Since O'S is estimated to the right , and O'S ' to the left , they have contrary signs ; hence , O'S = - O'S ' . But O'S is the co - tangent of OT , and O'S ...
Seite 47
... angle is equal to the sine of the opposite angle multiplied by the hypotenuse . 2. The sine of either acute angle is equal to the opposite side divided by the hypotenuse . Since the angles P and B are complements of each RIGHT TRIANGLES ...
... angle is equal to the sine of the opposite angle multiplied by the hypotenuse . 2. The sine of either acute angle is equal to the opposite side divided by the hypotenuse . Since the angles P and B are complements of each RIGHT TRIANGLES ...
Seite 48
... angle is equal to the tangent of the opposite angle multiplied by the other side . 6. The tangent of either acute angle is equal to the oppo- site side divided by the adjacent side . Since the angles P and B are complements of each ...
... angle is equal to the tangent of the opposite angle multiplied by the other side . 6. The tangent of either acute angle is equal to the oppo- site side divided by the adjacent side . Since the angles P and B are complements of each ...
Seite 49
... opposite side . BH BT :: BP BQ , or p : 1 :: h : sec B. PH : PN :: PB : PL , or b : 1 :: h : sec P. h h Ρ sec B sec B = ( 9 ) ( 10 ) p = h sec P h sec P b b 9. Either side adjacent to the right angle is equal to the hypotenuse divided ...
... opposite side . BH BT :: BP BQ , or p : 1 :: h : sec B. PH : PN :: PB : PL , or b : 1 :: h : sec P. h h Ρ sec B sec B = ( 9 ) ( 10 ) p = h sec P h sec P b b 9. Either side adjacent to the right angle is equal to the hypotenuse divided ...
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Häufige Begriffe und Wortgruppen
a. c. log adjacent angles adjacent side altitude angle is equal angle opposite applying logarithms arc increases arc is equal arc OT Article 98 circumscribed circle co-sine co-tangent co-versed-sine complement cos b cos cos² cosec decreases denote diagonal divided entire surface escribed circles Examples Find the angle find the area Find the logarithm fourth quadrant frustum functions given angle greater than 90 Hence hypotenuse included angle increases from 90 increases numerically inscribed log blog M.
M. Cosine M.
M. Sine mantissa minus Napier's principles negative number corresponding one-half the sum opposite angle perpendicular plane polygon positive Problem quadrant from H required the area right angle Right Triangles secant second quadrant side adjacent sin a sin slant height solution species spherical triangle supplement Tang tangent third quadrant triangle becomes Trigonometry versed-sine
Beliebte Passagen
Seite 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Seite 106 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Seite 122 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Seite 141 - 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...
Seite 17 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Seite 20 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 120 - The sines of the sides of a spherical triangle are proportional to the sines of their opposite angles. Let ABC be a spherical triangle.
Seite viii - For a number greater than 1, the characteristic is positive and is one less than the number of digits before the decimal point.
Seite 63 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Seite viii - In general, if the number is not an exact power of 10, its logarithm, in the common system, will consist of two parts — an entire part and a decimal part. The entire part is called the characteristic and the decimal part is called the mantissa.