Trigonometry for Beginners: With Numerous Examples

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Macmillan, 1866 - 192 páginas
 

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Página 166 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 10 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Página 31 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 92 - ... and 24° 19' respectively : how much higher is the cliff than the lighthouse ? Ans. 1942 feet. 77. A person standing on the bank of a river observes -.J ' the elevation of the top of a tree on the opposite bank to be 51...
Página 2 - French method, a right angle is divided into 100 equal parts called grades ; a grade into 300 equal parts called minutes ; a minute into 100 equal parts called seconds. The symbol for each is g V " ; as, for example, 12" 15V 754V means 12 grades, 15 minutes, 75 seconds.
Página 172 - To prove that if 6 be the circular measure of a positive angle less than a right angle, sin 6 lies between 6 and 6 -iff1.
Página 21 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Página 167 - To shew that the angle subtended at the centre of a circle by an arc equal to the radius of the circle if the same for all circles.
Página 32 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M—cf, then, raising both sides to the mth power, we have Mm = (a*)"1 = a™ . Therefore, log (Mm) = xm = (log M) X m.
Página 31 - Suppose a' = n, then x is called the logarithm of n to the base a; thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The logarithm of n to the base a is written Iog0 n ; thus loga n — x expresses the same relation as a1 = n.

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