## Plane Trigonometry, for Colleges and Secondary Schools |

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### Common terms and phrases

acute angle algebraic approximately base calculated called changes CHAPTER Check circle column Compare computation constructed containing cosē cosec cosine cotangent deduced definitions denoted Derive difference direction distance draw elevation equal equation EXAMPLES exercises expression figures Find formulas four geometry give given greater height Hence included increases inscribed known length less logarithms mantissa mathematics means measure method minutes namely negative NOTE observed obtained opposite perpendicular places plane polygon positive practical problems projection Prove quadrant quantities radian measure radius regular relations represented respectively right angles right-angled triangle Show shown sides sinē sine solution Solve student subtended tables taken taking tanē tangent tion tower triangle trigonometric functions trigonometric ratios Write

### Popular passages

Page 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.

Page 54 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.

Page 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.

Page 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.

Page vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.

Page 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.

Page 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.

Page 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.

Page 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.