## Plane and Spherical Trigonometry |

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### Common terms and phrases

a. c. log acute angle angle is equal angle opposite angular application base characteristic circle circular measure column complement computation Construct corresponding cos a cos cosine cotangent decimal definition denote determined difference distance divided draw EXERCISES expressed Find the angle Find the logarithm find the remaining formulas functions Given half the sum Hence hypothenuse integral length less less than 180 log h logarithm mantissa minus minutes natural negative obtained opposite opposite side perpendicular plane positive principles PROBLEM quadrant quantity quotient radius ratios reference represented result right angle right triangle root Scholium secant side sides adjacent signs sin A sin sine solution species spherical triangle square subtracted Suppose tabular tangent THEOREM tions unit vertical whence 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.