A Course of Mathematics: Composed for the Use of the Royal Military Academy |
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Page 557
... cosec . A. 6. Let a , b , c be the three sides of a triangle ; put h = b + c and k = b — c ; then will the area of the triangle be = 4√ ( h2 — a2 ) ( a2 — k2 ) . 7. Let the three sides be a , b , c ; then prove that the area of the ...
... cosec . A. 6. Let a , b , c be the three sides of a triangle ; put h = b + c and k = b — c ; then will the area of the triangle be = 4√ ( h2 — a2 ) ( a2 — k2 ) . 7. Let the three sides be a , b , c ; then prove that the area of the ...
Page 562
... cosec . and .. cosec . ( 90 ° - 0 ) = sec . 10. The versed sine of the complement of any angle 562 ANALYTICAL PLANE TRIGONOMETRY .
... cosec . and .. cosec . ( 90 ° - 0 ) = sec . 10. The versed sine of the complement of any angle 562 ANALYTICAL PLANE TRIGONOMETRY .
Page 565
... cosec . = sec . ( 90 ° 1 = cos . ( 90 ° by last case 1 = sin . or , cosec . ◊ sin . ◊≈ 1 ... ( 6 ) Since CAT is a right - angled triangle and CT the hypotenuse , CA2 + AT2 = CT 2 Dividing by CA2 , AT 2 CT 2 1+ = CA 2 CA 2 i . e . 1 + ...
... cosec . = sec . ( 90 ° 1 = cos . ( 90 ° by last case 1 = sin . or , cosec . ◊ sin . ◊≈ 1 ... ( 6 ) Since CAT is a right - angled triangle and CT the hypotenuse , CA2 + AT2 = CT 2 Dividing by CA2 , AT 2 CT 2 1+ = CA 2 CA 2 i . e . 1 + ...
Page 566
... cosec . sin . = 1 7 . 1 + tan . 20 sec . θ 2 8 . 1 + cot . 20 cosec . 24 9 . 10 . v . sin . coversin . = 1 cos . 6 = 1 . sin . . 11. The chord of an arc is the ratio of the straight line joining the two extre- mities of the arc to the ...
... cosec . sin . = 1 7 . 1 + tan . 20 sec . θ 2 8 . 1 + cot . 20 cosec . 24 9 . 10 . v . sin . coversin . = 1 cos . 6 = 1 . sin . . 11. The chord of an arc is the ratio of the straight line joining the two extre- mities of the arc to the ...
Page 568
... cosec . = sin . in like manner , the sign of the cosecant is always the same with that of the sine . The versed sine is always positive , being reckoned from A always in the same direction . P A C A It is sometimes convenient to give ...
... cosec . = sin . in like manner , the sign of the cosecant is always the same with that of the sine . The versed sine is always positive , being reckoned from A always in the same direction . P A C A It is sometimes convenient to give ...
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Common terms and phrases
axis become x becomes bisected called centre chord circle circumference co-ordinates Corol cosec cosine curve decimal denominator determine diameter difference differential co-efficient distance Divide divisor draw dx dy dy dx equal EXAMPLES expression feet figure formula fraction function greatest common measure Hence hyperbola inches latus rectum least common multiple logarithm manner monomial multiplied negative nth root opposite P₁ parallel parallelogram perpendicular polynomial positive Prob problem Prop proportional quotient radius ratio rectangle remaining right angles rule sides sine square root straight line Substituting subtract tangent Taylor's theorem THEOREM triangle ABC unknown quantity whence whole number yards