Plane Trigonometry for the Use of Students Preparing for Examinations: Containing the More Advanced Propositions, Solution of Problems and a Complete Summary of Formulae, Bookwork, Etc., Together with Recent Examination Papers for the Army, Woolwich, India, and Home Civil Services, Etc. With Answers
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Plane Trigonometry for the Use of Students Preparing for Examinations ...
A Dawson Clarke
No preview available - 2016
Plane Trigonometry, for the Use of Students Preparing for Examinations ...
A. Dawson Clarke
No preview available - 2017
ambiguous angle subtended base centre circle circumscribing circle inscribed circular measure circumscribed circles coefficient cos0 cos2 cos4 cosec cosine cot2 cotangent deduce diff equal escribed circles feet Find an expression find the angle Find the area find the value formula Francis Storr geometrical given log given sine given triangle horizontal plane included angle integer L sin L tan logarithms miles Moivre's Theorem number of degrees observes opposite angles Pedal triangle perpendicular Pkop plane triangle positive integer Prop Prove the following Prove the formula quadrant quadrilateral radii regular polygon respectively satisfy the equation sec2 secant sign and magnitude sin0 sin2 sin4 sine sine and cosine solution Solve the equation solve the triangle straight line subtends an angle tan2 tan4 tangent tower Trace the changes triangle ABC triangle in terms trig-ratios trigonometrical functions trigonometrical ratios unit of circular yards
Page 296 - 2 A. 3. Find a general expression for all the angles which have the same tangent as a given angle. Solve the equation— * 4. If A + B be less than a right angle, prove, by means of geometrical figures, the formulae— sin (A + B) = sin A cos B + cos A sin B, sin A + sin B=2 sin
Page 53 - Since sin 18° is +, we take the upper sign, .'. sin 18° (ii.) Geometrically. = cos 72°. Let ABC be a triangle having each of the angles at the base double of the angle at the vertex.
Page 186 - XIII. 1. The angle subtended at the centre of a circle by an arc which is equal in length to the radius is invariable. Express in degrees and circular measure the vertical angle of an isosceles triangle -which is half of each of the angles at the base. * 2. Investigate an expression which shall include all angles that have a given cosine. 3. Prove the following
Page 206 - XXXII. 1. Assuming that a circle may be treated as a regular polygon with an infinite number of sides, show that the ratio of the circumference of a circle to its diameter is constant. What is the circular measure of the least angle whose sine is — , and what is the measure in degrees, etc., of 2 the angle whose circular measure is
Page 228 - 26c cos A, and apply it to prove that if the straight line which bisects the vertical angle of a triangle also bisects the base, then the triangle must be isosceles. 9. Find the area of a triangle in terms of the sides. 10. Find the radius of the circle which touches one side of a triangle
Page 297 - when expressed in terms of sin A, has four values. 7. Prove that in a triangle the sides are proportional to the sines of the opposite angles. If, in a triangle ABC,
Page 209 - and 45° respectively, and the length of the side opposite to the latter is a furlong. Show that the field contains exactly two acres and a half. 10. Find an expression for the diameter of the circle which touches one side of a triangle and the other sides produced. If
Page 272 - cos (A - B) = cos A cos B + sin A sin B, and show that, if the tangent of one angle of a triangle be equal to the sum of the sines of the other two, the tangents of the halves of the angles will be in geometrical progression. 2. Find an expression for the area of a