## Trigonometry for Beginners |

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affection algebraically Atan base called centre CHAPTER characteristic circle contains corresponding cos² cosec cosine cot log cot decimal definition determined difference direction distance draw equal equation EXAMPLE EXERCISE Express feet Find the number foot formulæ four fraction functions geometrical given greater half height Hence increases integral length less than 90 log cos log cot log log tan log logarithm magnitude means measure miles minutes negative observed obtain opposite perpendicular places plane positive Prove quadrant radians radius ratios represented respectively right angles Show sides Similarly sin B sin sin² sine solution Solve the triangle spherical triangle stands student subtended Suppose tangent tower triangle trigonometrical ratios unit XOP₁ yards

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Page 85 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant figure.

Page 6 - A radian is an angle at the center of a circle, subtended by an arc equal in length to the radius of the circle.

Page 25 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?

Page 122 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 82 - Whence x + y is the logarithm of mn. q. BD 10. Prop. 2. — Tlie logarithm of the quotient of two numbers is the logarithm, of the dividend minus the logarithm of the divisor.

Page iii - ... are not as many figures in the quotient as there are ciphers annexed to the dividend. In such a case, supply the deficiency, as in the division of decimals, by prefixing a cipher or ciphers to the quotient before annexing.

Page 135 - Two solutions exist so long as both values of c are positive, and less than 180°, that is, so long as sin c is positive. Now when a differs more from 90° than b, we have (neglecting the signs for a moment), cos a > cos...

Page 115 - Express in degrees, minutes, etc., (i.) the angle whose circular measure is -^tr; (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°. 3. If esc A = 9, find cot A and sec A . 4.

Page 82 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.

Page 113 - A° in circular measure. 2. Define the sine, secant, and cotangent of an angle, and express any two of these ratios in terms of the third. Find the trigonometrical ratios of the angle whose cosine isf.