## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 73

Page 215

...

...

**tang**AM , or**tang**ACM , CT sec AM , or sec ACM , AP - ver - sin AM , or ver - sin ACM . 1 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 ... Page 217

...

...

**tang**90o - ∞ The complement of 90 ° being zero , we have**tang**0 = cot 90 ° and cot 0 =**tang**90o . Hence 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 : i 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 ...### Other editions - View all

### Common terms and phrases

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