Trigonometric equations (or called goniometric equations) are those equations - matlab homework help - in which the unknown occurs in the argument of angular functions.
cos x = 0.5; sin x = 0.702;
tan x = 1.39; cos x + cos 2x = 1
In these examples, the task is to find the angle x in degrees or radians that satisfies the equation.
Solving trigonometric equations means determining angular quantities that satisfy the equation - do your homework . For simple cases that occur quite frequently in practice, however, solutions can be found by clever reshaping. Often, however, one has to use suitable approximation methods.
In cases where one knows some values of angular functions, one can give a solution immediately.
Since cos 60°=0.5, one can state for cos x = 0.5 that the solution is
The number of solutions is determined by the given interval - https://domyhomework.club/accounting-homework/. Since the trigonometric functions are periodic, one finds another solution in the interval [0; 2 π] with cos x=cos (360°- x), i.e. x2=300°.
If all solutions (independent of a certain interval) are required, then because of the periodicity the following applies
x1=π/3+2 kπ and x2=5π/3+2 kπ , where k is any integer.
It should also be noted whether the solution specifications are to be given in degrees or radians.
If radians are required, the solutions from the interval are called [0; 2 π]:
x1=60° corresponds to x1=π3 andx2=300° corresponds to x2=5π3.
The solution set can be understood by drawing the graph of the cosine function and a parallel to the x-axis at a distance of 0.5.
The abscissa values of the intersections of this parallel with the cosine curve provide just the x-values for our example equation, which satisfy the equation.