A trigonometric equation values of given trigonometric functions whose arguments are unknown angles. The task is to determine all possible values of those angles. For obtaining the solution one needs the following properties of the trigonometric functions:
Two angles have the same value of cosine iff the angles are equal or opposite (http://planetmath.org/OppositeNumber) angles or differ of each other by a multiple of full angle.
Two angles have the same value of cotangent iff the angles are equal or differ of each other by a multiple of straight angle.
The first principle in solving a trigonometric equation is that try to elaborate with goniometric formulae or else it so that only one trigonometric function on one angle remains in the equation. Then the equation is usually resolved to the form
where and are known numbers and is one of the functions sin, cos, tan, cot. Thereafter one can solve the values of the angle and, dividing these by , at last the values of the angle .
On the third line one used the double angle formula of sine.
It may happen that the form (1) cannot be attained, but instead e.g. the form
where can be in .
On the second line one of the complement formulas was utilized.
On the second line the opposite angle formula (http://planetmath.org/GoniometricFormulae) of sine was utilized.
On the second line the supplement formula (http://planetmath.org/GoniometricFormulae) of sine was utilized.
|Date of creation||2013-03-22 17:46:25|
|Last modified on||2013-03-22 17:46:25|
|Last modified by||pahio (2872)|