A Treatise on Elementary TrigonometryMacmillan, 1892 - 306 páginas |
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Página 8
... Show that the perpendicular drawn from the right angle to the hypotenuse in an isosceles right - angled triangle , each of whose equal sides contains a feet , is √2 a ft . 2 • ( 10 ) If the hypotenuse of a right - angled isosceles ...
... Show that the perpendicular drawn from the right angle to the hypotenuse in an isosceles right - angled triangle , each of whose equal sides contains a feet , is √2 a ft . 2 • ( 10 ) If the hypotenuse of a right - angled isosceles ...
Página 39
... Show that the measure of the angle at the centre of a circle of radius r , which stands on an arc a , is depends solely on the unit of angle employed . k.a Find k when the unit is ( i ) a radian , ( ii ) a degree . g " where k * 72 ...
... Show that the measure of the angle at the centre of a circle of radius r , which stands on an arc a , is depends solely on the unit of angle employed . k.a Find k when the unit is ( i ) a radian , ( ii ) a degree . g " where k * 72 ...
Página 41
... show that the mean angle is 60o . ( 7 ) The three angles of a triangle are in arithmetical pro- gression , and the number of grades in the least is to the number of degrees in the mean as 5 : 6. Find the angles in degrees . ( 8 ) The ...
... show that the mean angle is 60o . ( 7 ) The three angles of a triangle are in arithmetical pro- gression , and the number of grades in the least is to the number of degrees in the mean as 5 : 6. Find the angles in degrees . ( 8 ) The ...
Página 42
... Show that the number of degrees in an angle of a regular decagon is to the number of grades in an angle of a regu- lar pentagon in the ratio of 6 : 5 . ( 19 ) Show that the number of grades in an angle of a regular pentagon is equal to ...
... Show that the number of degrees in an angle of a regular decagon is to the number of grades in an angle of a regu- lar pentagon in the ratio of 6 : 5 . ( 19 ) Show that the number of grades in an angle of a regular pentagon is equal to ...
Página 52
... show that sin2 A + cos2 A = 1 , and that sin2 B + cos2 B = 1 . ( 6 ) If ABC be any right - angled triangle with a ... Show that sin A α = - с b cos A = tan A = с Show also that sin2 A + cos2 A = 1 . α Show also that ( i ) a = c . sin A ...
... show that sin2 A + cos2 A = 1 , and that sin2 B + cos2 B = 1 . ( 6 ) If ABC be any right - angled triangle with a ... Show that sin A α = - с b cos A = tan A = с Show also that sin2 A + cos2 A = 1 . α Show also that ( i ) a = c . sin A ...
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Términos y frases comunes
algebraical angle of elevation angle ROP angular arithmetical base centre circular measure circumference circumscribing circumscribing circles common logarithms cos² cos³ cosec cosine cosine and tangent decimal described diameter distance distant object equal Express find log Find the angle Find the height Find the length Find the number find the sine formulæ fraction geometrically given that log greater Hence horizontal hypotenuse inches initial line inscribed circle isosceles triangle less Let ROP magnitude miles negative number of degrees observed opposite perimeter perpendicular positive Prove the following Quadrant radians radius regular polygon respectively revolving line right angle right-angled triangle sec² sides significant figures sin² sin³ sine square student subtended tan² tangent telescope Theodolite tower Trace the changes triangle ABC Trigono Trigonometrical Ratios vernier yards ОР
Pasajes populares
Página 14 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 12 - A trapezoid has only two of its sides parallel ; as ABCD. (Fig. 4.) Any other four sided figure is called a trapezium. II. A figure which has more than four sides is called a polygon. A regular polygon has all its sides equal, and all its angles equal. III. The height of a triangle is the length of a perpendicular, drawn from one of the angles to the opposite side ; as CP. (Fig. 5.) The height of a four sided figure is the perpendicular distance between two of its parallel sides ; as CP.
Página 274 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 59 - 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 ? 8.
Página 129 - T' formulae. 2 sin A . cos B = sin (A + B) + sin (A -B), ' 2 cos A . sin B = sin (A + B) — sin (A - B), h 1v.
Página 30 - VI. 33) angles at the centre of the same circle are to one another as the arcs on which they stand...
Página 225 - The elevation of a steeple at a place due south of it is 45°, and at another place due west of it the elevation is 15°. If the distance between the two places be a, prove that the height of the steeple is a( \/3 — 1) -^2\/3.
Página 242 - Now, twice the area of a polygon circumscribed about a circle is equal to (the radius x the perimeter).
Página 256 - Prove that sin (A + B) = sin A cos B + cos A sin B, and deduce the expression for cos (A + B).
Página 288 - Show how to solve a triangle when two sides and the included angle are given. If two sides of a triangle are 71 and 25 feet and the contained angle 69° 32...