Plane and Spherical Trigonometry |
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Page 6
... Determine the algebraic signs of 1. cos 218 ° . 2. tan ( -460 ° ) . 3. sin 1100 ° . 4. cot ( -99 ° ) . 5. sec 315 ° . 6. csc ( — 210 ° ) . 7. Let the student determine , as above , the signs of the trigono 77. Functions of Acute Angles ...
... Determine the algebraic signs of 1. cos 218 ° . 2. tan ( -460 ° ) . 3. sin 1100 ° . 4. cot ( -99 ° ) . 5. sec 315 ° . 6. csc ( — 210 ° ) . 7. Let the student determine , as above , the signs of the trigono 77. Functions of Acute Angles ...
Page 14
... determine the relations which exist among the functions of two angles when those angles are related in some par- ly P x ' Τα α P M X M α X x ' M α P ' M ** P α FIG . 8 . ticular way . Let us consider first two angles one of which is the ...
... determine the relations which exist among the functions of two angles when those angles are related in some par- ly P x ' Τα α P M X M α X x ' M α P ' M ** P α FIG . 8 . ticular way . Let us consider first two angles one of which is the ...
Page 15
... determined by the quadrant which in when a is acute . 16. Functions of 90 ° a . a lies Consider next two angles , α and 90 ° a , Fig . 9. Let XOP be the angle a and XOP ' be 90 ° α . Lay off on the terminal sides of these angles the ...
... determined by the quadrant which in when a is acute . 16. Functions of 90 ° a . a lies Consider next two angles , α and 90 ° a , Fig . 9. Let XOP be the angle a and XOP ' be 90 ° α . Lay off on the terminal sides of these angles the ...
Page 19
... determined by the quad- rant ( counting in the positive direction ) in which the terminal side of the angle lies when a is acute . Examples . 1. sin ( 720 ° — α ) = sin α , since 720 ° is an even multiple of 90 ° and the terminal side ...
... determined by the quad- rant ( counting in the positive direction ) in which the terminal side of the angle lies when a is acute . Examples . 1. sin ( 720 ° — α ) = sin α , since 720 ° is an even multiple of 90 ° and the terminal side ...
Page 70
... determine which value is correct or whether both are possible we recall the theorem of geometry which states that if the given angle is acute and the side opposite is less than the other given side , then it may be possible to construct ...
... determine which value is correct or whether both are possible we recall the theorem of geometry which states that if the given angle is acute and the side opposite is less than the other given side , then it may be possible to construct ...
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Common terms and phrases
13 co-function 15 read 9 Prop abscissa angle of elevation angle XOP antilogarithms axis base bottom c d L Ctn characteristic colog cologarithm column COMMON LOGARITHMS computation cos² cotangent Ctn c d decimal places decimal point distance equations Example exponent feet Find the value formulæ hence L Cos d L Sin d law of cosines law of sines log cot log csc log sin Log10 Value Log10 loga loge Logo Value mantissa miles multiple negative OA OA opposite ordinate perpendicular polar triangle positive quadrant radians radius read as printed read co-function result right triangles sec² significant figures sin b sin sin² SOLUTION OF RIGHT spherical triangle tabular difference tan-¹ tan² tangent terminal side theorem tion trigonometric functions Va² Value Log10 Value Value Logo Whence write zero
Popular passages
Page 71 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. 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. By Theorem II. we have a : b : : sin. A : sin. B.
Page 151 - I. The logarithm of a product is equal to the sum of the logarithms of the factors : log ab = log a + log b. This follows from the fact that if 10¡ = a and lO1- = 6, 101+£ = a • b.
Page 98 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Page 151 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 34 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 129 - The spherical excess of any spherical polygon is equal to the excess of the sum of its angles over two right angles taken as many times as the polygon has sides, less two.
Page xx - The proportional parts are stated in full for every tenth at the right-hand side The logarithm of any number of four significant figures can be read directly by addN...
Page 35 - The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root.
Page 97 - But a' = 180° - a, c' = 180° - c, and CAB' = 180° - A Hence cos (180° — a) =cos b cos (180° - c) + sin b sin (180° - c) cos (180a- A)9 or, cos a = cos b cos с -f- sin b sin с cos A, which- proves the law of cosines for all cases.
Page 32 - ... consists of two parts, an integral part and a decimal part. The integral part is called the characteristic of the logarithm, and may be either positive or negative.