General Solutions
Each of the trigonometric functions is periodic in the real part of its argument, running through all its values twice in each interval of 2π. Sine and cosecant begin their period at 2πk − π/2 (where k is an integer), finish it at 2πk + π/2, and then reverse themselves over 2πk + π/2 to 2πk + 3π/2. Cosine and secant begin their period at 2πk, finish it at 2πk + π, and then reverse themselves over 2πk + π to 2πk + 2π. Tangent begins its period at 2πk − π/2, finishes it at 2πk + π/2, and then repeats it (forward) over 2πk + π/2 to 2πk + 3π/2. Cotangent begins its period at 2πk, finishes it at 2πk + π, and then repeats it (forward) over 2πk + π to 2πk + 2π.
This periodicity is reflected in the general inverses where k is some integer:
- Which, written in one equation, is:
- Which, written in one equation, is:
Read more about this topic: Inverse Trigonometric Functions
Famous quotes containing the words general and/or solutions:
“Some people are under the impression that all that is required to make a good fisherman is the ability to tell lies easily and without blushing; but this is a mistake. Mere bald fabrication is useless; the veriest tyro can manage that. It is in the circumstantial detail, the embellishing touches of probability, the general air of scrupulous—almost of pedantic—veracity, that the experienced angler is seen.”
—Jerome K. Jerome (1859–1927)
“Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not.”
—Isaac Asimov (1920–1992)