Plane Trigonometry, for Colleges and Secondary Schools |
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Page xi
... law of sines . The law of cosines . · 54a . Substitution of sines for sides , and of sides for sines 46 97 98 101 55. Case I. Given one side and two angles 101 . 56. Case II . 57. Case III . Given two sides and an angle opposite to one ...
... law of sines . The law of cosines . · 54a . Substitution of sines for sides , and of sides for sines 46 97 98 101 55. Case I. Given one side and two angles 101 . 56. Case II . 57. Case III . Given two sides and an angle opposite to one ...
Page 98
... law of sines . The law of cosines . I. The law of sines . From C in the triangle ABC draw CD at right angles to opposite side AB , and meeting AB or AB produced in D. ( In Fig . 47 a B is acute , in Fig . 47b B is obtuse , and in A 4 4 ...
... law of sines . The law of cosines . I. The law of sines . From C in the triangle ABC draw CD at right angles to opposite side AB , and meeting AB or AB produced in D. ( In Fig . 47 a B is acute , in Fig . 47b B is obtuse , and in A 4 4 ...
Page 99
... sines of the opposite angles . Each of the fractions in ( 1 ) gives the length of the diameter of the circle described about ABC . Let O ( Fig . 48 ) be the centre and R the radius of the circle described about ABC . Draw ... LAW OF SINES .
... sines of the opposite angles . Each of the fractions in ( 1 ) gives the length of the diameter of the circle described about ABC . Let O ( Fig . 48 ) be the centre and R the radius of the circle described about ABC . Draw ... LAW OF SINES .
Page 189
... Law of Sines for the plane triangle . ( b ) State and prove the Law of Cosines for the plane triangle . ( c ) If the sines of the angles of a triangle are in the ratios of 13 : 14 : 15 , prove that the cosines are in the ratios of 39:33 ...
... Law of Sines for the plane triangle . ( b ) State and prove the Law of Cosines for the plane triangle . ( c ) If the sines of the angles of a triangle are in the ratios of 13 : 14 : 15 , prove that the cosines are in the ratios of 39:33 ...
Page 190
Daniel Alexander Murray. 8. Assuming the law of sines for a plane triangle , prove that a + b : c = cos ( AB ) : sin C , and a − b : c = sin 1 ( A – B ) : cos 1⁄2 C. - 2:34 , prove 2 cos = A a + c 2 b ( b ) If 2 a = b + c , 9. ( a ) If ...
Daniel Alexander Murray. 8. Assuming the law of sines for a plane triangle , prove that a + b : c = cos ( AB ) : sin C , and a − b : c = sin 1 ( A – B ) : cos 1⁄2 C. - 2:34 , prove 2 cos = A a + c 2 b ( b ) If 2 a = b + c , 9. ( a ) If ...
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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'.