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a. c. log acute angle added adjacent side angle greater angle is equal angle opposite angular base characteristic circle column complement computation Construct corresponding cos x cos cosecant cosine cotangent coversed decimal definition denote determined difference distance divided draw EXERCISES expressed Find the angle find the number find the remaining formulas functions Given half the sum Hence horizontal hypothenuse included less less than 180 log h logarithm mantissa minus negative opposite opposite side perpendicular plane positive PROBLEM quadrant quantity quotient radius ratios Required Required Required result right angle right triangle root Scholium secant side sides adjacent signs sin A sin sine solution species spherical triangle square subtracted tabular tangent THEOREM tions triangle unit vers vertical whence x cos y
Page 145 - 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 142 - 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 140 - Any angle is greater than the difference between 180° and the sum of the other two angles.
Page 147 - 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 127 - 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 47 - ... 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 156 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 98 - ... 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.