Plane and Spherical Trigonometry |
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Page 14
... figure , MIPI = OP M2P2 OP2 M3P3 = = etc. = sin 0 , OP3 OM1 OM 2 = = OM 3 = etc. cos 0 , OP1 OP2 OP3 M1P1 M2P2 M3P3 = = = etc. = tan 0 , OM1 OM2 OM 3 and similarly for the other trigonometric ratios . Hence the six ratios remain ...
... figure , MIPI = OP M2P2 OP2 M3P3 = = etc. = sin 0 , OP3 OM1 OM 2 = = OM 3 = etc. cos 0 , OP1 OP2 OP3 M1P1 M2P2 M3P3 = = = etc. = tan 0 , OM1 OM2 OM 3 and similarly for the other trigonometric ratios . Hence the six ratios remain ...
Page 27
... figures of Art . 11 , it is evident that for an angle . angle in any quadrant ( 1 ) 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 ...
... figures of Art . 11 , it is evident that for an angle . angle in any quadrant ( 1 ) 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 ...
Page 40
... These agree to four significant figures . The formula sin B = b could also be used in checking . * Results to be inserted when work is completed . Example 2. Given a 6.72 and b = = Solution 40 PLANE TRIGONOMETRY Vectors.
... These agree to four significant figures . The formula sin B = b could also be used in checking . * Results to be inserted when work is completed . Example 2. Given a 6.72 and b = = Solution 40 PLANE TRIGONOMETRY Vectors.
Page 52
... figures , there is no necessity to compute accurately to more figures than this . If the measuring instrument can be read only to minutes of angle , in the computation , there is no object in carrying the work to seconds of angle . 38 ...
... figures , there is no necessity to compute accurately to more figures than this . If the measuring instrument can be read only to minutes of angle , in the computation , there is no object in carrying the work to seconds of angle . 38 ...
Page 62
... figures triangles OMP , OHD , and OEF are similar . Assume that HD is positive when measured upward , and negative when measured downward ; also that EF is positive when measured to the right , and negative when measured to the left ...
... figures triangles OMP , OHD , and OEF are similar . Assume that HD is positive when measured upward , and negative when measured downward ; also that EF is positive when measured to the right , and negative when measured to the left ...
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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.