## Plane and Spherical Trigonometry |

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### Common terms and phrases

a+ẞ acute angle adapted to logarithmic angle of elevation celestial celestial sphere chord circle circle of latitude circular measure colog complement cosc cosecant cosine cotangent csc q ctn A ctn deduced denote distance equator Example feet find the angle find the functions find the height following angles formulas Geometry Given a leg given angle headland horizon initial line less than 180 log csc log ctn log s-a log sin logarithmic logarithmic computation meas method miles negative OBLIQUE TRIANGLES obtained OC X base perp Plane Trig positive Prove quad quadrant radius right angle right triangle sec q secant sides sin a sin sine and cosine solution spherical triangle SPHERICAL TRIGONOMETRY ẞ ctn substituting tan(A+B tan² tangent terminal line tions triangle of reference trigonometric functions α+β β² ов хор

### Popular passages

Page 15 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.

Page 73 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 73 - 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 93 - From a station B at the base of a mountain its summit A is seen at an elevation of 60°; after walking one mile towards the summit up a plane making an angle of 30° with the horizon to another station C, the angle BCA is observed to be 135°.

Page 7 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 77 - Formulas for the area of a triangle, in terms of two sides and the included angle ; in terms of one side and the adjacent angles; and in terms of s and the three sides.

Page 22 - 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 51 - SJ, St. Louis Univ. : I have given the book a thorough examination, and I am satisfied that it is the best work on the subject I have seen. I mean the best work for what it was intended, — a textbook. I would like very much to introduce it in the University. (Jan.