Pure mathematics, Τόμος 11874 |
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Σελίδα 336
... sine of an arc BC is the perpen- dicular from one extremity , C , of the arc upon the diameter passing through the other extremity B. B Thus CS is the SINE of the arc BC . ( 2. ) The cosine of an arc is the sine of the complement of the ...
... sine of an arc BC is the perpen- dicular from one extremity , C , of the arc upon the diameter passing through the other extremity B. B Thus CS is the SINE of the arc BC . ( 2. ) The cosine of an arc is the sine of the complement of the ...
Σελίδα 337
... sine falls , which is included between the sine and the extremity of the arc . Thus , SB is the VERSED SINE of the arc BC . ( 8. ) The coversed sine is the versed sine of the complement of the arc . Thus , S'D is the COVERSED SINE of ...
... sine falls , which is included between the sine and the extremity of the arc . Thus , SB is the VERSED SINE of the arc BC . ( 8. ) The coversed sine is the versed sine of the complement of the arc . Thus , S'D is the COVERSED SINE of ...
Σελίδα 340
Edward Atkins. 7. To express the trigonometrical ratios in terms of the sine . ( 1. ) Cos A = ( 2. ) Tan A = = √1 sin A , by Art . 6 ( 6. ) 1 sin A cos A ' by Art . 6 ( 9. ) , sin A √1 - sin2 A ( 3. ) Cot A = = ( 4. ) Sec A = cos A sin ...
Edward Atkins. 7. To express the trigonometrical ratios in terms of the sine . ( 1. ) Cos A = ( 2. ) Tan A = = √1 sin A , by Art . 6 ( 6. ) 1 sin A cos A ' by Art . 6 ( 9. ) , sin A √1 - sin2 A ( 3. ) Cot A = = ( 4. ) Sec A = cos A sin ...
Σελίδα 342
... sine sin o ) ( a sine sin o + r cos ◊ sin 4 ) = r sin ◊ ( r cos e + a sine ) . - rsin e cos p , Y = r sin e sin p , ≈ = 15. If x that x + y2 + 22 1 2.2 . 16. If a = b cos C + c cos B , b r cose , show = a cos C + c cos A , = c = a ...
... sine sin o ) ( a sine sin o + r cos ◊ sin 4 ) = r sin ◊ ( r cos e + a sine ) . - rsin e cos p , Y = r sin e sin p , ≈ = 15. If x that x + y2 + 22 1 2.2 . 16. If a = b cos C + c cos B , b r cose , show = a cos C + c cos A , = c = a ...
Σελίδα 345
... sine changes in magnitude from 0 to 1 and is + . The cosine changes in magnitude from 1 to 0 and is + . The tangent ... sine , cosine , and tangent respec- tively , when the angle is indefinitely diminished . Hence the sine during the ...
... sine changes in magnitude from 0 to 1 and is + . The cosine changes in magnitude from 1 to 0 and is + . The tangent ... sine , cosine , and tangent respec- tively , when the angle is indefinitely diminished . Hence the sine during the ...
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a²b a²b² ab² ab³ ABCD algebraical angle ABC angle BAC angle BCD base BC BC is equal bisect brackets cent centim centre circle ABC circumference coefficient common Const cosec cube root decimal figures denominator divided divisor draw equation expression exterior angle factor Find the value fraction given straight line gnomon gram greater Hence integer join kilom less Let ABC logarithm metres miles millig Multiply opposite angles parallel parallelogram perpendicular PROOF.-Because Q. E. D. Proposition quotient ratio rectangle contained remainder right angles segment sides sin² sine square on AC square root subtraction touches the circle triangle ABC twice the rectangle x²y² x³y xy³
Δημοφιλή αποσπάσματα
Σελίδα 272 - The angles in the same segment of a circle are equal to one another.
Σελίδα 103 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 233 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let A and BC be two straight lines, and let BC be divided into any...
Σελίδα 112 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 128 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 119 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Σελίδα 113 - ... equal angles in each ; then shall the other sides be equal, each to each ; and also the third angle of the one to the third angle of the other.
Σελίδα 273 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.
Σελίδα 281 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 121 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.