Plane Trigonometry with Tables |
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Page 33
... cota , we have cos2 α COS a • COS α sin a cos2 a cot a cos a cot a + cos α sin a cos a cos a ( 1 + sin a ) + cos a sin a sin a 1 sin2 a 1 sin a cos a ( 1 + sin a ) COS α Now multiply the numerator and denominator by 1- sin a cot a COS α ...
... cota , we have cos2 α COS a • COS α sin a cos2 a cot a cos a cot a + cos α sin a cos a cos a ( 1 + sin a ) + cos a sin a sin a 1 sin2 a 1 sin a cos a ( 1 + sin a ) COS α Now multiply the numerator and denominator by 1- sin a cot a COS α ...
Page 96
... cota + tan ß sin a cosẞ Proof . Express cot a and tan ẞ in terms of sine and cosine ; then cos a cota + tan ẞ 15. cot 0 tan α = sin B + sin a cos B cos ( 0 + α ) cos a cos ẞ + sin a sin ß sin a cos B cos ( a B ) sin a cos ẞ MM sin e cos ...
... cota + tan ß sin a cosẞ Proof . Express cot a and tan ẞ in terms of sine and cosine ; then cos a cota + tan ẞ 15. cot 0 tan α = sin B + sin a cos B cos ( 0 + α ) cos a cos ẞ + sin a sin ß sin a cos B cos ( a B ) sin a cos ẞ MM sin e cos ...
Page 98
... cota + 2 sin a cos a = sec a csc a . sin2 a ( 1 + cos2 a ) 20. sec2 a cos2 α = 1 + sin a 21 . sin a 22. sec1 a 23. Given al2 cos 0 + bl cos 0 sin a + 1 - sin a sec2 α = tan2 a + tan4 a . cos2 a = sec2 a ( csc a + 1 ) . = co , and an212 ...
... cota + 2 sin a cos a = sec a csc a . sin2 a ( 1 + cos2 a ) 20. sec2 a cos2 α = 1 + sin a 21 . sin a 22. sec1 a 23. Given al2 cos 0 + bl cos 0 sin a + 1 - sin a sec2 α = tan2 a + tan4 a . cos2 a = sec2 a ( csc a + 1 ) . = co , and an212 ...
Page 7
... a = log ( 90 ° - a ) " + S. log ( 90 ° — a ) " + T . log ( 90 ° — a ) ' ' = - log tan a = cpl log ( 90 ° — a ) " + cpl T. cpl log cot a . log cos a + cpl S. log cota + cpl T. cpl log tan a + cpl T. 9.99 0 " IO " 20 " 30 " 40 53.
... a = log ( 90 ° - a ) " + S. log ( 90 ° — a ) " + T . log ( 90 ° — a ) ' ' = - log tan a = cpl log ( 90 ° — a ) " + cpl T. cpl log cot a . log cos a + cpl S. log cota + cpl T. cpl log tan a + cpl T. 9.99 0 " IO " 20 " 30 " 40 53.
Common terms and phrases
½ π 9 Prop abscissa acute angle amplitude angle of elevation base cd log cot colog cologarithm complex number computations coördinates cos² cos³ cosh cosine cot cd log cot² cotangent cpl log decimal Draw equal equation Example Express figures Find the angle Find the area Find the number Find the value formulas given hyperbolic functions imaginary unit log cot cd log cot log log tan cd log tan log loga loge M₁P₁ Mant mantissa measured miles per hour modulus multiples negative nth root number corresponding ordinate P₁ positive Prove radians radius right triangle root sec² segment sin a sin sin ß sin² sin³ sine sinh Solution Solve subtract tabular difference tan² tangent terminal side theorem trigonometric functions unit circle vector vertical α α
Popular passages
Page 2 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 139 - The cube root of a number is one of the three equal factors of the number. Thus the cube...
Page 101 - CASE II. Given two sides and an angle opposite one of them. CASE III.
Page 13 - 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.
Page 101 - In any triangle the sides are proportional to the sines of the opposite angles.
Page ii - Electrical World The Engineering andMining Journal Engineering Record Engineering News Railway Age Gazette American Machinist Signal Engineer American Engineer Electric Railway Journal Coal Age Metallurgical and Chemical Engineering Power ANALYSIS BY EDWARD G.
Page 4 - In it the right angle is divided into 100 equal parts called grades, the grade into 100 equal parts called minutes, and the minute into 100 equal parts called seconds.
Page 110 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 14 - The logarithm of the reciprocal of a number is called the Cologarithm of the number.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.