## Formulas and theorems in pure mathematics |

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Page 161

The secant, cosecant, and cotangent of 180°— A, and of —A, will follow the same

rule as their reciprocals, the cosine,

any ratio of an angle greater than 90° to the ratio of an angle less than 90°.

The secant, cosecant, and cotangent of 180°— A, and of —A, will follow the same

rule as their reciprocals, the cosine,

**sine**, and tangent. [610 — 612 625 To reduceany ratio of an angle greater than 90° to the ratio of an angle less than 90°.

Page 187

II.

we can take A, B, c instead of their complements, and change

vice versd, for those parts at once. Thus, taking b for the middle part, sin b = tan a

...

II.

**sine**of -middle part = product of cosines of opposite parts. In applying the ruleswe can take A, B, c instead of their complements, and change

**sine**into cos, orvice versd, for those parts at once. Thus, taking b for the middle part, sin b = tan a

...

Page 188

2 v sin ft

where , = j(«+ft+e). 2 v sin* sin (*— a) v ' Proof. — sin'— = | (1— cos A). Substitute

for cobA from (872), and throw the numerator of the whole expression into ...

2 v sin ft

**sine**885 cos 4= ^"n* «in (»-«). 2 v sin 6**sine**886 tanj = Vii"^6.) s'n (*~c)where , = j(«+ft+e). 2 v sin* sin (*— a) v ' Proof. — sin'— = | (1— cos A). Substitute

for cobA from (872), and throw the numerator of the whole expression into ...

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### Contents

Introduction The C G S System of Units | 1 |

VHI Common and Hyperbolic Logarithms of | 7 |

QUANT1C8 1620 | 30 |

Copyright | |

108 other sections not shown

### Common terms and phrases

becomes Binomial Theorem bisect changes of sign chord circumscribing circle columns conic conjugate constant continued fraction convergent cosec cosine curve denoted determinant diameter divided eliminant ellipse equal equate coefficients expand factors figure formula function given circle given ratio Hence hyperbola imaginary roots infinite inscribed circle integer integral intersect inverse points limits logarithm method Multiply negative nine-point circle notation obtained orthogonally pair parabola parallel partial fractions perpendicular plane positive powers Proof Proof.—By Proof.—In Proof.—Let Proof.—The quantic quantities quotient radical axis radius respect result right angle rows Rule sides similar triangles Similarly sine singular solution solution squares substituting successive tangent Taylor's theorem theorem tion transformed triangle ABC unity vanishes variables zero