## Plane and Spherical Trigonometry |

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### Common terms and phrases

3d quadrant a+ẞ acute angle angle or arc angle xop asin B₁ base celestial celestial sphere centre chord circle of latitude circular measure colog complement Compute cosecant cosine cotangent csc q ctn a ctn ctn q deduce denote direction distance equator Example figures find the angle find the functions following angles formulas functions of 90 Geometry given angle horizon hypothenuse initial line less than 180 log csc log sin logarithmic meas method miles negative obtained OC'B perp perpendicular Plane Trig positive Prove quad right angle right triangle rotation sec q secant sin a sin sinē sine and cosine solution solve spherical triangle SPHERICAL TRIGONOMETRY ẞ ctn straight line substituting tanē tangent terminal line tions triangle of reference trigonometric functions vertex α α ов ос

### 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 51 - Price, $1.90; for introduction, $1.80. rPHIS book is written especially for those who have had no previous knowledge of the subject, and is therefore adapted to self-instruction as well as to the needs of the class-room. The subject is at first presented in a very simple manner. As the reader advances, less and less attention is given to details. Throughout the entire work it is the constant aim to arouse and enliven the reader's interest, by first showing how the various concepts have arisen naturally,...

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 48 - Taylor's Calculus was found to be in use in about sixty colleges. The Nation, New York: In the first place, it is evidently a most carefully written book.... We are acquainted with no text-book of the Calculus which compresses so much matter into so few pages, and at the same time leaves the impression that all that is necessary has been said. In the second place, the number of carefully selected examples, both of those worked out in full in illustration of the text, and of those left for the student...

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 20 - 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 47 - 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.