Plane Trigonometry, for Colleges and Secondary Schools |
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Page xi
... formulas for all values of the two angles 49. Each fundamental formula contains the others 50. Ratios of an angle in terms of the ratios of its half angle 888 89 90 90 51. Tangents of the sum and difference of two angles , and of twice ...
... formulas for all values of the two angles 49. Each fundamental formula contains the others 50. Ratios of an angle in terms of the ratios of its half angle 888 89 90 90 51. Tangents of the sum and difference of two angles , and of twice ...
Page 42
... also be wrong . Hence it is advisable to check the values found by seeing whether they satisfy relations differing from those already employed . For example , check formulas which may be used in 42 [ CH . III . PLANE TRIGONOMETRY .
... also be wrong . Hence it is advisable to check the values found by seeing whether they satisfy relations differing from those already employed . For example , check formulas which may be used in 42 [ CH . III . PLANE TRIGONOMETRY .
Page 43
... formulas is necessary in cases in which the answers are not given . The test- ing of the results also affords practice in the use of formulas and in computation . When a check formula is satisfied it is highly probable , but not ...
... formulas is necessary in cases in which the answers are not given . The test- ing of the results also affords practice in the use of formulas and in computation . When a check formula is satisfied it is highly probable , but not ...
Page 44
... Formulas : tan A a ( 1 ) b B 90 ° . = b Checks : tan B - C = α sin A A. ( 2 ) ( 3 ) α a2 = c2 - b2 = ( c + b ) ( c − b ) . * This is to be filled after the values of the unknown quantities have been found . It is advisable to indicate ...
... Formulas : tan A a ( 1 ) b B 90 ° . = b Checks : tan B - C = α sin A A. ( 2 ) ( 3 ) α a2 = c2 - b2 = ( c + b ) ( c − b ) . * This is to be filled after the values of the unknown quantities have been found . It is advisable to indicate ...
Page 45
... formula tan B b = - а can be used instead of ( 2 ) . A check then is A + B = 90 ° . Instead of ( 3 ) , one of the following formulas can be used , viz . b C = b sin B ' α C = cos B C = COS A There is often a choice of formulas that can ...
... formula tan B b = - а can be used instead of ( 2 ) . A check then is A + B = 90 ° . Instead of ( 3 ) , one of the following formulas can be used , viz . b C = b sin B ' α C = cos B C = COS A There is often a choice of formulas that can ...
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Common terms and phrases
A+B+C acute angle algebraic angle of elevation central angle CHAPTER circle circumscribing cologarithm column computation cos² cosec cotangent deduced denoted Derive draw equal equation EXAMPLES expression figures find log Find the angle Find the distance Find the height find the number formulas geometrical Given log graph Hence Hipparchus hypotenuse inverse trigonometric functions isosceles triangle law of sines length M₁ mantissa mantissa of log mathematics method negative NOTE number of degrees number of sides OP₁ perpendicular proj Prove radian measure radius regular polygon revolving right angles right-angled triangle sec² secant Show shown sin² sin³ sine and cosine Solve spherical trigonometry subtended tan-¹ tan² tangent terminal line theorems tower triangle ABC trigono trigonometric functions trigonometric ratios turning line whole number X₁
Popular passages
Page 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.
Page 54 - 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, F = \ ab.
Page 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Page vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.
Page 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.
Page 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Page 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Page 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.