A Treatise on Elementary TrigonometryMacmillan, 1892 - 306 páginas |
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Página 57
... lies on a circle whose centre is 0 . Then if the angle ROP be diminished , we can see that MP is diminished also , and that consequently MP " OP which is sin ROP , is diminished . And , by diminishing the angle ROP sufficiently , we can ...
... lies on a circle whose centre is 0 . Then if the angle ROP be diminished , we can see that MP is diminished also , and that consequently MP " OP which is sin ROP , is diminished . And , by diminishing the angle ROP sufficiently , we can ...
Página 58
... lies on a circle whose centre is 0 . Then , as the angle ROP approaches to ROU , we can see that MP approaches OP , while OM continually diminishes . Hence when ROP approaches 90 ° , sin ROP , which is OP OP 1 1 approaches in value to ...
... lies on a circle whose centre is 0 . Then , as the angle ROP approaches to ROU , we can see that MP approaches OP , while OM continually diminishes . Hence when ROP approaches 90 ° , sin ROP , which is OP OP 1 1 approaches in value to ...
Página 92
... lies always on the circumference of a circle whose centre is 0 . Let this circle cut the lines LOR , UOD in the points L , R , U , D respectively . The circle RULD is thus divided at the points R , U , L , D into four Quadrants , of ...
... lies always on the circumference of a circle whose centre is 0 . Let this circle cut the lines LOR , UOD in the points L , R , U , D respectively . The circle RULD is thus divided at the points R , U , L , D into four Quadrants , of ...
Página 102
... lies between 0 ° and 90 ° . We now give some examples of a method of proving the truth of this and other like formulæ , whatever be the magnitude of the angle concerned . Example 1. To prove that the sine of an angle = the cosine of its ...
... lies between 0 ° and 90 ° . We now give some examples of a method of proving the truth of this and other like formulæ , whatever be the magnitude of the angle concerned . Example 1. To prove that the sine of an angle = the cosine of its ...
Página 145
... lie between 90 ° and 180o . ( 3 ) For the ( A + B ) formulæ , when A lies between 90 ° and 180o , and ( A + B ) lies between 180o and 270o . - ( 4 ) For the ( 4 – B ) formulæ , when A lies between 180 ° and 270 ° , and ( A - B ) lies ...
... lie between 90 ° and 180o . ( 3 ) For the ( A + B ) formulæ , when A lies between 90 ° and 180o , and ( A + B ) lies between 180o and 270o . - ( 4 ) For the ( 4 – B ) formulæ , when A lies between 180 ° and 270 ° , and ( A - B ) lies ...
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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...