Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of ComputationH. Holt, 1882 - 104 páginas |
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Página 19
Simon Newcomb. EXERCISES . Prove the following expressions for the trigonometrical func- tions of angles of more than 90 ° by the necessary diagrams . The angle x may be supposed less than 90 ° , though this restriction is not necessary ...
Simon Newcomb. EXERCISES . Prove the following expressions for the trigonometrical func- tions of angles of more than 90 ° by the necessary diagrams . The angle x may be supposed less than 90 ° , though this restriction is not necessary ...
Página 29
... expression for the angle corresponding to a given function , add an arbitrary number of circumferences to the angles found in the last section . Then the most general expression for angles which have the same sine will be nC + 90 ° + a ...
... expression for the angle corresponding to a given function , add an arbitrary number of circumferences to the angles found in the last section . Then the most general expression for angles which have the same sine will be nC + 90 ° + a ...
Página 30
... expression for all angles having the same cosine . 9. Form the most general expression for all angles having the same tangent . Relations between the Six Trigonometric Functions . 33. When we know any one trigonometric function of an ...
... expression for all angles having the same cosine . 9. Form the most general expression for all angles having the same tangent . Relations between the Six Trigonometric Functions . 33. When we know any one trigonometric function of an ...
Página 32
... Expression of each function in terms of the others . By means of the relations ( 1 ) to ( 4 ) any one trigonometric function may be expressed in terms of any other by algebraic substitutions . The following are the expressions which we ...
... Expression of each function in terms of the others . By means of the relations ( 1 ) to ( 4 ) any one trigonometric function may be expressed in terms of any other by algebraic substitutions . The following are the expressions which we ...
Página 37
... expression . In the accom- panying figure OQN , ONP , and OXN are right angles , and we put α = angle XON ; Bangle NOQ . It will also be noticed that Angle XNP = α and Angle ONX = XPN = 90 ° — a . 90 N 00 X P. It is now required to ...
... expression . In the accom- panying figure OQN , ONP , and OXN are right angles , and we put α = angle XON ; Bangle NOQ . It will also be noticed that Angle XNP = α and Angle ONX = XPN = 90 ° — a . 90 N 00 X P. It is now required to ...
Otras ediciones - Ver todas
Elements of Plane and Spherical Trigonometry with Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2016 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2018 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2017 |
Términos y frases comunes
9 Prop algebraic sign angle AOB angle corresponding angle XOM applied arithmetical complement circle circumference co-log co-ordinates coefficients column computation cos² cos³ cosec cosine cotangent Cotg differences distance divided Entering the table equal equations error example EXERCISES expression find log find the values formula fourth quadrant geometry gives greater Hence interpolation intersect latitude length line OX log cot measure metres minutes nth roots perpendicular places of decimals polar triangle polygon preceding problem projection quantities radius revolving right angle right triangle roots of unity secant sides sin a cos sin a sin sin² sine N sines and cosines spherical triangle spherical trigonometry square substituting subtract suppose Tang theorem third quadrant tions trigono trigonometric functions trihedral angle unit write wwww zero ΙΟ
Pasajes populares
Página 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 4 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 66 - 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 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 34 - To find the trigonometric functions corresponding to an angle between 45° and 90°, we take the degrees at the bottom of the page and the minutes in the right-hand column. The values of the...
Página 139 - 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 132 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Página 44 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles.
Página 73 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Página 53 - Conventionally the period is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds.