Trigonometry for Beginners: With Numerous Examples |
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1+cos A-sin A+B+C AB sin angle BAC angle increases angle PAB angles in terms AP AP AP coincides AP moves centre circle circular measure cos² cos³ cosec cosine cotangent decimal decreases numerically deduced determine distance divided draw PM perpendicular equal equation Euclid example express feet figure in Art find log find the height Find the number formulæ four right angles given angle Given log Hence hypotenuse known L sin minutes number of degrees number of grades observe the angle opposite PM AP polygon preceding Article present Chapter quadrant PM regular polygon right-angled triangle sec² secant sexagesimal shew sides sin A cos sin A sin sin² sine solve a triangle straight line drawn Suppose tangent tower triangle having given Trigono Trigonometrical Ratios vers yards ОР
Popular passages
Page 166 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 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.
Page 31 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 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...
Page 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.
Page 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.
Page 21 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 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.
Page 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.
Page 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.