## Elements of Trigonometry: Plane and Spherical |

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Adding adjacent angle or arc angled spherical triangle apply base becomes column comp complement compute considered Construct corresponding cosec cosine cotangent cotx determine diameter difference distance divided draw equal example EXERCISES extremes fall feet figure Finally Find the angles formula given gives greater hence hypotenuse increase known less less than 180 limit log cos log cot log sin LOGARITHMIC FUNCTIONS manner means measuring multiple Napier's natural negative oblique angle observe obtain opposite passing perpendicular plane triangle positive preceding Prob produce project the triangle proposition quadrant radius relations represent right angled triangle rules secant side similar sin a sin sine solution solve the triangle species student subtract tan x tang tangent trigonometrical functions values whence

### Popular passages

Page 95 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 94 - In, any 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 two sides into the cosine of their included angle.

Page 72 - The last statement involves the assertion that the three angles of a spherical triangle determine the sides, whereas we are accustomed to say in Plane Trigonometry, that, at least one given part of a plane triangle must be a side, in order that the triangle may he determined- There is really no such difference as these two statements imply- For example, it...

Page 19 - The sine of the difference of any two arcs or angles is equal to the sine of the first into the cosine of the second, minus the cosine of the first into the sine of the second.

Page 60 - Parallels, which are imaginary circles parallel with the equator, determine latitude. The length of a degree of longitude varies as the cosine of the latitude. At the equator a degree is 69.171 statute miles; this is gradually reduced toward the poles.

Page 62 - AC and the angles. 9. From the top of a mountain, three miles high, the angle of depression of a line tangent to the earth's surface is taken, and found to be 2° 13

Page 62 - What was the perpendicular height of a balloon, when its angles of elevation were 35° and 64°, as taken by two observers...