Plane and Spherical Trigonometry

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Ginn, Heath & Company, 1882 - Trigonometry - 201 pages

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Page 128 - V-- 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite to the side a, prove that 2 _ 8. Prove that in any plane triangle C* ~~i
Page 68 - That is : The area of a triangle is equal to half the product of two sides and the sine of the included angle.
Page 20 - Geometry that 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...
Page v - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Page 23 - From the top of a hill the angles of depression of two objects situated in the...
Page 52 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Page 111 - A very simple relation exists between the hour angle of the sun and the local (apparent) time of day. Since the hourly rate at which the sun appears to move from east to west is 15°, and it is apparent noon when the sun is on the meridian of a place, it is evident that if hour angle = 0°, 15°, — 15°, etc., time of day is noon, 1 o'clock PM, 11 o'clock AM, etc. In general, if t...
Page 132 - Express in degrees, minutes, etc., (i.) the angle whose circular measure is -fair; (ii.) the angle whose circular measure is 5. If the angle subtended at the centre of a circle by the side of a regular pentagon be the unit of angular measurement, by what number is a right angle represented? 2. Find, by geometrical constructions, the cosine of 45° and the sine of 120°. Prove that (sin 30° + cos 30°) (sin 120° + cos 120°) = sin 30°.
Page 106 - The vertical circle passing through the east and west points of the horizon is called the Prime Vertical; that passing through the north and south points coincides with the celestial meridian.
Page 127 - A 6. Express the cosine of half an angle in terms of the sine of the angle, and explain the double sign. Employ the formula to find the value of cos 75°, having given sin 150° = ^. 7. If A, B, C be the angles of a triangle, and a, b, c the sides respectively opposite to them, show that J Af bo where s = one-half the sum of the sides.

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