Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 páginas |
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Página 29
... measured by that arc . Thus , MT , the sine of the arc OT , is the sine of the angle OCT , which is measured by the arc OT ; and similarly for the other arcs and angles . The arcs OT and OT ' are in the first and second quadrants ...
... measured by that arc . Thus , MT , the sine of the arc OT , is the sine of the angle OCT , which is measured by the arc OT ; and similarly for the other arcs and angles . The arcs OT and OT ' are in the first and second quadrants ...
Página 36
... measured by these equal arcs , are equal . The angles CO'S and CO'S ' are equal , since each is a right angle . Hence , the two triangles CO'S and CO'S ' have the common side CO ' , and the two adjacent angles equal , and are therefore ...
... measured by these equal arcs , are equal . The angles CO'S and CO'S ' are equal , since each is a right angle . Hence , the two triangles CO'S and CO'S ' have the common side CO ' , and the two adjacent angles equal , and are therefore ...
Página 37
... measured by TO , is equal to the angle OCT , measured by the equal arc OT . The right angles COR and COR ' are equal . Hence , in the triangles having the common FUNCTIONS . 37 The secant of an arc.
... measured by TO , is equal to the angle OCT , measured by the equal arc OT . The right angles COR and COR ' are equal . Hence , in the triangles having the common FUNCTIONS . 37 The secant of an arc.
Página 39
... measured by the arc O'T , is equal to the angle O'CT ' , measured by the equal arc O'T ' . The right angles , COS and CO'S ' , are equal . Hence , in the triangles having the common side CO ' , and the two adjacent angles equal , CS is ...
... measured by the arc O'T , is equal to the angle O'CT ' , measured by the equal arc O'T ' . The right angles , COS and CO'S ' , are equal . Hence , in the triangles having the common side CO ' , and the two adjacent angles equal , CS is ...
Página 64
... measured by the intercepted arc AE . The inscribed angle ADE is measured by one - half the arc AE ; hence , ADE ACE = ¦ ( A + B ) . - → CH CA , since they are hence , the angle CHA A. exterior to the triangle CHB hence , radii of the ...
... measured by the intercepted arc AE . The inscribed angle ADE is measured by one - half the arc AE ; hence , ADE ACE = ¦ ( A + B ) . - → CH CA , since they are hence , the angle CHA A. exterior to the triangle CHB hence , radii of the ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 106 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 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.
Página 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...
Página 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.
Página 20 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 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.
Página viii - For a number greater than 1, the characteristic is positive and is one less than the number of digits before the decimal point.
Página 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.
Página 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.