Elements of Geometry and Trigonometry |
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Page 209
... tang AM , or tang ACM , CT sec AM , or sec ACM , AP - ver - sin AM , or ver - sin ACM . VI . Having taken the arc AD equal to a quadrant , from the points M and D draw the lines MQ , DS , perpendicular to the radius CD , the one ...
... tang AM , or tang ACM , CT sec AM , or sec ACM , AP - ver - sin AM , or ver - sin ACM . VI . Having taken the arc AD equal to a quadrant , from the points M and D draw the lines MQ , DS , perpendicular to the radius CD , the one ...
Page 210
... tang 0 = 0 , cos 0 = R , sec 0 = R . VIII . As the point M advances towards D , the 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 ...
... tang 0 = 0 , cos 0 = R , sec 0 = R . VIII . As the point M advances towards D , the 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 ...
Page 211
... tang 90 ° — ∞ The complement of 90 ° being zero , we have Hence tang 0 = cot 90 ° and cot 0 = tang 90o . cot 90 ° = 0 , and cot 0 = ∞ . X. The point M continuing to advance from D towards B , the sines diminish and the cosines ...
... tang 90 ° — ∞ The complement of 90 ° being zero , we have Hence tang 0 = cot 90 ° and cot 0 = tang 90o . cot 90 ° = 0 , and cot 0 = ∞ . X. The point M continuing to advance from D towards B , the sines diminish and the cosines ...
Page 212
... tang 180 ° -0 . When the point M ' passes the point B , and comes into the position N ' , the tangent of the arc ADN ' will be the line AT : hence , the tangents of all arcs which terminate in 212 PLANE TRIGONOMETRY .
... tang 180 ° -0 . When the point M ' passes the point B , and comes into the position N ' , the tangent of the arc ADN ' will be the line AT : hence , the tangents of all arcs which terminate in 212 PLANE TRIGONOMETRY .
Page 213
... tang 270 ° = ∞ . When the point has passed along into the fourth quadrant to N , the tangent of the arc ADN'N will ... tang ( x ) = - tang x cot -x ) = — cot x By considering the arc AM , and its supplement AM PLANE TRIGONOMETRY . 213.
... tang 270 ° = ∞ . When the point has passed along into the fourth quadrant to N , the tangent of the arc ADN'N will ... tang ( x ) = - tang x cot -x ) = — cot x By considering the arc AM , and its supplement AM PLANE TRIGONOMETRY . 213.
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex