Military examinations. Mathematical examination papers, set at entrance to the Royal military college, Sandhurst, with answers, by W.F. Austin |
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Results 1-5 of 9
Page 5
... tangent and cotangent of an angle . Express the values of cot 90 ° , tan 180 ° , tan 270 ° . Show that the tangent of any angle will have the same sign as its cotangent . Prove tan 45 ° = 1 and sec 45 ° 11 √2 . 12. Prove by means of a ...
... tangent and cotangent of an angle . Express the values of cot 90 ° , tan 180 ° , tan 270 ° . Show that the tangent of any angle will have the same sign as its cotangent . Prove tan 45 ° = 1 and sec 45 ° 11 √2 . 12. Prove by means of a ...
Page 8
... rule for finding its value adapted to the other measure . Express in foreign measure each angle of the isosceles triangle described in Euclid's 10th proposition , Book IV . 9. Show how to express the cosine , tangent , ( 8 )
... rule for finding its value adapted to the other measure . Express in foreign measure each angle of the isosceles triangle described in Euclid's 10th proposition , Book IV . 9. Show how to express the cosine , tangent , ( 8 )
Page 9
... tangent , and secant of an angle in 3 terms of the sine . The sine of an angle less than 90 ° is find 5 ' cosine , tangent , and secant . 10. Investigate the formula for sin ( A - B ) in terms of the sines and cosines of ( A ) and ( B ) ...
... tangent , and secant of an angle in 3 terms of the sine . The sine of an angle less than 90 ° is find 5 ' cosine , tangent , and secant . 10. Investigate the formula for sin ( A - B ) in terms of the sines and cosines of ( A ) and ( B ) ...
Page 13
... tangent of an angle , express in terms of it the other trigonometrical ratios of the angle . 9. Establish the formulæ ( 1. ) cos A – cos B = 2 sin + sin A + B 2 ( 2. ) cos 3A = 4 cos 3A - 3 cos A ; B - A ; 2 and employ ( 2 ) to obtain ...
... tangent of an angle , express in terms of it the other trigonometrical ratios of the angle . 9. Establish the formulæ ( 1. ) cos A – cos B = 2 sin + sin A + B 2 ( 2. ) cos 3A = 4 cos 3A - 3 cos A ; B - A ; 2 and employ ( 2 ) to obtain ...
Page 16
... tangent meeting the other chord ( produced , if necessary ) , then will the two chords , and the segment intercepted between the parallels , be proportional . 9. Trace the changes of sign of sin 0 , as increases through four right ...
... tangent meeting the other chord ( produced , if necessary ) , then will the two chords , and the segment intercepted between the parallels , be proportional . 9. Trace the changes of sign of sin 0 , as increases through four right ...
Other editions - View all
Military Examinations. Mathematical Examination Papers, Set at Entrance to ... Sandhurst Roy Military Coll No preview available - 2015 |
Military Examinations. Mathematical Examination Papers, Set At Entrance To ... Sandhurst Roy Military Coll No preview available - 2023 |
Military Examinations. Mathematical Examination Papers, Set At Entrance To ... Sandhurst Roy Military Coll No preview available - 2023 |
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Popular passages
Page 44 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 24 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, is equal to the square of the line which touches it.
Page 36 - 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.
Page 12 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 2 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Page 36 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Page 36 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 44 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 2 - ... the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
Page 2 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.