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A+B+C acute angles algebraic centre CHAPTER circumscribing computation cosē cosec cosine cotangent deduced denoted Derive diedral angle draw equal equation EXAMPLES expression figure Find the distance formulas geometry given height Hence hypotenuse included angle inscribed circle intersection inverse trigonometric functions isosceles triangle law of cosines law of sines length logarithms M₁ method negative NOTE number of degrees number of sides opposite perpendicular Plane Trigonometry polar triangle pole positive quadrant QUESTIONS AND EXERCISES radian measure radii radius regular polygon relations respectively revolving right angles right-angled triangle secē secant Show sides and angles sinē sine solid angle Solve ABC sphere spherical angle spherical degree spherical excess spherical polygon spherical triangle spherical trigonometry subtended surface tanē tangent terminal line triangle ABC triedral trigonometric functions trigonometric ratios whole number
Page 35 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Page 87 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 85 - 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 and the cosine of their included angle.
Page 55 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 111 - The ratio of a circumference of a circle to its diameter is the same for all circles. [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance, to Euclid VI., 33.* The proof of (6) is not contained in all geometries ; for instance, Euclid does not give...
Page 183 - 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.