Elements of Geometry and Trigonometry |
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Page 215
... 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 216
... 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 217
... 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 increase ...
... 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 increase ...
Page 218
... 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 218 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 218 PLANE TRIGONOMETRY .
Page 219
... 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 . 219.
... 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 . 219.
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang 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 parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
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Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
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Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
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