Trigonometry for Beginners: With Numerous Examples

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Macmillan, 1866 - 192 стор.

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Сторінка 164 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Сторінка 32 - The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number by the index of the power. For let m = a"; therefore m' = (a")
Сторінка 144 - B + cos A sin B. sin (A - B) = sin A cos B - cos A sin 1?. cos (A + B) = cos A cos B - sin A sin B. cos (A - B) = cos A cos B + sin A sin B.
Сторінка 31 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Сторінка 31 - The Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number. Thus if m = a", x is called the logarithm of m to the base a.
Сторінка 90 - At the foot of a mountain the elevation of its summit is found to be 45°. After ascending for one mile, at a slope of 15°, towards the summit, its elevation is found to be 60° : find the height of the mountain.
Сторінка 21 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Сторінка 53 - To solve a triangle having given two sides and the angle opposite to one of them. Let a and b be the given sides, and A the given angle ; then - . — -. = - ; therefore sin B = - sin A ; aa therefore L sin B = log b - log a •+- L sin A.
Сторінка 91 - A tower is situated on the top of a hill whose angle of inclination to the horizon is 30°. The angle subtended by the tower at the foot of the hill is found by an observer to be 15°; and on ascending 485 feet up the hill the tower is found to subtend an angle of 30° : find (1) the height of the tower, and (2) the distance of its base from the foot of the hill.
Сторінка 135 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles themselves.

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