Elements of Geometry and Trigonometry |
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Page 215
... cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS cot AM , or cot ACM , CS = cosec AM , or cosec ACM . In general , A being any arc or angle , we have cos A sin ( 90 ° —A ) , cot A = tang ...
... cotangent , and cosecant , of the arc AM , and are thus designated : MQ = cos AM , or cos ACM , DS cot AM , or cot ACM , CS = cosec AM , or cosec ACM . In general , A being any arc or angle , we have cos A sin ( 90 ° —A ) , cot A = tang ...
Page 216
... 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 complement MD , the sine MP is equal to the cosine MQ or CP ; and the trian- gle CMP ...
... 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 complement MD , the sine MP is equal to the cosine MQ or CP ; and the trian- gle CMP ...
Page 219
... cotangent is infinite ; when at E it is zero : hence , cot 180 ° = = - ; cot 270 ° = 0 . Let 9 stand for a quadrant ; then the following table will show the signs of the trigonometrical lines in the different quadrants . Sine Cosine ...
... cotangent is infinite ; when at E it is zero : hence , cot 180 ° = = - ; cot 270 ° = 0 . Let 9 stand for a quadrant ; then the following table will show the signs of the trigonometrical lines in the different quadrants . Sine Cosine ...
Page 222
... cotangent , and cosecant of the same arc . The triangles CPM , CAT , CDS , being similar , we have the proportions : CP : PM :: CA : AT ; or cos A : sin A :: R : tang A CP : CM :: CA : CT ; or cos A : R :: R : sec A = = PM : CP :: CD ...
... cotangent , and cosecant of the same arc . The triangles CPM , CAT , CDS , being similar , we have the proportions : CP : PM :: CA : AT ; or cos A : sin A :: R : tang A CP : CM :: CA : CT ; or cos A : R :: R : sec A = = PM : CP :: CD ...
Page 223
... cotangent to R. COS COS SIL 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 ...
... cotangent to R. COS COS SIL 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 ...
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adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex