Plane and Spherical Trigonometry |
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៦៩៩៦ a. c. log acute angle adjacent angle adjacent side angle greater angle is equal angle opposite circular measure column common logarithm cos b cos cosecant cosine cotangent degrees and minutes denote EXERCISES Find the angle Find the logarithm find the number find the remaining formulas given angle given number Given Required given side half the sum Hence hypothenuse included angle intercepted arc less than 180 Let ABC log h mantissa negative number of degrees number whose logarithm opposite angle opposite side opposite the given perpendicular plane triangle quadrant quotient radius ratios right angle right triangle Scholium secant sides adjacent sin A sin sin x cos sin² sine solution species spherical triangle subtracted tangent THEOREM VIII triangle is equal triangle of reference trigonometric functions versed sine whence x cos y ΙΟ
Popular passages
Page 147 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 57 - 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 144 - 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 142 - Any angle is greater than the difference between 180° and the sum of the other two angles.
Page 149 - С . cos A = — cos B . cos С + sin B . sin С . cos « . III. cos B = — cos A . cos С + sin A . sin С . cos ß . cos G = — cos A . cos B...
Page 129 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 49 - ... base is to the sum of the other two sides, as the difference of those sides is to the difference of the segments of the base.
Page 158 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 100 - ... b) = sec b, cosec ( — b) = — cosec b ; (53) that is, the cosine and secant of the negative of an angle are the same as those of the angle itself ; and the sine, tangent, cotangent, and cosecant of the negative of an angle are the negatives of those of the angle. These results correspond with those obtained geometrically (Art. 68). 80.