Plane trigonometry, by S.L. Loney.

CONTENTS.
CHAP.
XXIII. Expansions of sin na, cos nO, and tan nO
Expansions of sin a and cos a in a series of ascending
powers of a
Sines and Cosines of small angles.
Approximation to the root of an equation
Evaluation of indeterminate quantities
XXIV. Expansions of cos" 0 and sin 60 in cosines or sines of
multiples of.
Expansions of sin nO and cos nO in series of descending and ascending powers of sin 6 and cos.

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XXV. Exponential Series for Complex Quantities
Circular functions of complex angles
Euler's exponential values
Hyperbolic Functions.
Inverse Circular and Hyperbolic Functions
XXVI. Logarithms of complex quantities.
Value of ax when a and x are complex
XXVII. Gregory's Series.
Calculation of the value of r.
XXVIII. Summation of Series
Expansions in Series.
XXIX. Factors of x2- 2xn cos n6 + 1
Factors of xn- 1 and x" + 1
Resolution of sin 6 and cos 6 into factors
sinh 6 and cosh 0 in products
XXX. Principle of Proportional Parts
XXXI. Errors of observation
XXXII. Miscellaneous Propositions
Solution of a Cubic Equation
Maximum and Minimum Values
Geometrical representation of complex quan
Miscellaneous Examples..

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tities. 472
477