Elements of Geometry and Trigonometry |
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Page 215
... like manner , be the sine , tangent , and secant of the arc MD , the complement of AM . For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , ...
... like manner , be the sine , tangent , and secant of the arc MD , the complement of AM . For the sake of brevity , they are called the cosine , cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , ...
Page 216
... sine increases , and so likewise does the tangent and the secant ; but the cosine , the cotangent , and the cosecant , diminish . When the point M is at the middle of AD , or when the arc AM is 45 ° , in which case it is equal to its ...
... sine increases , and so likewise does the tangent and the secant ; but the cosine , the cotangent , and the cosecant , diminish . When the point M is at the middle of AD , or when the arc AM is 45 ° , in which case it is equal to its ...
Page 219
... cotangent is infinite ; when at E it is zero : hence , cot 180 ° - = ; cot 270 ° = 0 . Let q stand for a quadrant ; then the following table will show the signs of the trigonometrical lines in the different quadrants . Sine Cosine Tangent ...
... cotangent is infinite ; when at E it is zero : hence , cot 180 ° - = ; cot 270 ° = 0 . Let q stand for a quadrant ; then the following table will show the signs of the trigonometrical lines in the different quadrants . Sine Cosine Tangent ...
Page 222
... cos A = ± √ ( R2 - sin2A ) , and sin A = ± √ ( R2 — cos2A ) . The sign of these formulas is + , or because the same sine MP answers to the two arcs AM , AM ' , whose cosines CP , CP ' , are equal and have contrary signs ; and the same ...
... cos A = ± √ ( R2 - sin2A ) , and sin A = ± √ ( R2 — cos2A ) . The sign of these formulas is + , or because the same sine MP answers to the two arcs AM , AM ' , whose cosines CP , CP ' , are equal and have contrary signs ; and the same ...
Page 223
... cotangent to R.Cos COS Sin it follows that tangent and cotangent will both be positive when the sine and cosine have like algebraic signs , and both negative , when the sine and cosine have contrary algebraic signs . Hence , the tangent ...
... cotangent to R.Cos COS Sin it follows that tangent and cotangent will both be positive when the sine and cosine have like algebraic signs , and both negative , when the sine and cosine have contrary algebraic signs . Hence , the tangent ...
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adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex