## The Elements of Plane and Spherical Trigonometry |

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The Elements of Plane and Spherical Trigonometry (Classic Reprint) Eugene Lamb Richards No preview available - 2017 |

### Common terms and phrases

A B C acute angle adjacent angle opposite base Books centre circle circular measure consider cosecant cosine cotangent Denote difference divided draw drawn English equal equation EXAMPLE express falls figure formed four given given angle given side greater half hemisphere History hypotenuse increases known length less less than 90 limit meet middle negative numerical value obtain obtuse angle opposite perpendicular plane polar positive produced proved quantity radius represent respectively right angle right-angled triangle secant seconds side side opposite similar manner sine solutions solve the triangle sphere spherical triangle straight line substituting supplement Suppose surface tables tangent third triangle of reference trigonometric functions trigonometric ratios unit VIII

### Popular passages

Page 54 - When the given angle is acute, and the side apposite the given angle is less than the other given side, and greater than the shortest dis.

Page 47 - 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 83 - In the circular measure of an angle and its intercepted arc, the unit of angle is an angle at the centre of a circle, subtended by an arc equal to the radius of the circle ; and this arc is the unit of arc.

Page 120 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 46 - For, since C is a right angle, its sine is 1 (Art. 35). Also 49. In any 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 68 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles themselves.

Page 72 - Express the cosine of the difference of two angles in terms of the sines and cosines of these angles.

Page 85 - A = a ; that is, the circular measure of any angle, at the centre of a circle whose radius is unity, is equal to the length of the arc subtending that angle.