Plane and Spherical Trigonometry |
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Page 2
... divide the plane formed by a complete revolution of the generating line into four parts by the two perpendicular lines X'X and Y'Y . These parts are called first , second , third , and fourth quadrants , respectively . They are placed ...
... divide the plane formed by a complete revolution of the generating line into four parts by the two perpendicular lines X'X and Y'Y . These parts are called first , second , third , and fourth quadrants , respectively . They are placed ...
Page 10
... divide the plane into four quad- rants , numbered as in Art . 3 . Any point P1 in the plane is located by the segments NP1 and MP1 drawn parallel to X'X and Y'Y respectively , for the values of these segments tell how far and in what ...
... divide the plane into four quad- rants , numbered as in Art . 3 . Any point P1 in the plane is located by the segments NP1 and MP1 drawn parallel to X'X and Y'Y respectively , for the values of these segments tell how far and in what ...
Page 27
... Dividing ( 1 ) by r2 , x2 + y2 = r2 . = .1 % = 1 . + But ニ= cos 0 and = sin 0 . [ 1 ] ..sin2 + cos2 0 = 1 . y2 Dividing ( 1 ) by x2 , 1+ = p.2 • But tan 0 У T = and sec = - [ 2 ] .. x2 Dividing ( 1 ) by y2 , +1 y2 x 1 + tan20 sec2 0 ...
... Dividing ( 1 ) by r2 , x2 + y2 = r2 . = .1 % = 1 . + But ニ= cos 0 and = sin 0 . [ 1 ] ..sin2 + cos2 0 = 1 . y2 Dividing ( 1 ) by x2 , 1+ = p.2 • But tan 0 У T = and sec = - [ 2 ] .. x2 Dividing ( 1 ) by y2 , +1 y2 x 1 + tan20 sec2 0 ...
Page 79
... Dividing by and substituting OB = 1 , AD = sin 0 , and BE = tan 0 , [ 12 ] sin 0 < 0 < tan 0 . Dividing [ 12 ] by sin and remembering that tan 0 1 < < sec 0 . sin 0 sin 0 - cos 0 ' Now as approaches 0 as a limit sec @ approaches 1 as a ...
... Dividing by and substituting OB = 1 , AD = sin 0 , and BE = tan 0 , [ 12 ] sin 0 < 0 < tan 0 . Dividing [ 12 ] by sin and remembering that tan 0 1 < < sec 0 . sin 0 sin 0 - cos 0 ' Now as approaches 0 as a limit sec @ approaches 1 as a ...
Page 80
... dividing [ 12 ] by tan 0 and simplifying , 0 cos @ < tan 0 < 1. But lim 0 ÷ 0 cos 0 = 1 , therefore lim Ө • = 0 tan 0 = 1 . By computing the following table the student will find the theorem verified for several angles . Angle in ...
... dividing [ 12 ] by tan 0 and simplifying , 0 cos @ < tan 0 < 1. But lim 0 ÷ 0 cos 0 = 1 , therefore lim Ө • = 0 tan 0 = 1 . By computing the following table the student will find the theorem verified for several angles . Angle in ...
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Common terms and phrases
9 Prop acute angle amplitude base cd log cot circle co-a co-c co-ẞ colog cologarithm complex number Computation coördinates cos(a cos¹ cos² cos³ cosh cosine cot cd log cotangent cpl log d log tan distance equal equation Example EXERCISES Express figures Find the logarithm find the mantissa Find the number Find the value formulas Given horizontal hyperbolic functions imaginary unit included angle interpolating log cot cd log cot log log tan cd log tan log loga Mant mantissa miles modulus multiples Napier's rules negative nth root number corresponding plane polar triangle positive Prove radians radius right spherical triangle right triangle root sec² sin a sin sin ẞ sin² sine sinh Solution Solve sphere Spherical Trigonometry Subtracting tabular difference tan-¹ tan² tangent terminal side theorem trigonometric functions z₁ απ
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 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 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 6 - When the number is greater than 1, the characteristic is positive, and is one less than the number of digits to the left of the decimal point...
Page 15 - To find any power of a given number, multiply the logarithm of the number by the exponent of the power. The product is the logarithm of the power.
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 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 161 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Page 14 - The logarithm of the reciprocal of a number is called the Cologarithm of the number.