Solving Trigonometric Problems

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Keeping in mind that 5pi over 6 is pi minus pi over 6 so this is the supplement.

That gives us a second solution, now I call these two solutions pi over 6 and 5pi over 6 my principle solutions and I want to get the rest of them by using the periodicity of the sine function.

Trigonometry is the study of relationships that deal with angles, lengths and heights of triangles and relations between different parts of circles and other geometrical figures.

Applications of trigonometry are also found in engineering, astronomy, Physics and architectural design.

It will have infinitely many points and there are going to be two points per period so expect infinitely many answers and expect to have two per period going into the problem.

Now usually I actually find the solutions on the unit circle, so I've drawn a unit circle and I've also drawn the line y equals one half because remember if I draw an angle the point on the unit circle where the angle crosses that point p its y coordinate is going to be the sine of this angle so in this case the y coordinate it's going to have to be one half so the question is what is this angle theta?Remember when you're solving equations, you're trying to find the values of the variable that make the equation true so we want to find all the angles for which the sine is one half.Now I've drawn the picture a graph of y equals sine theta and I want to show you that I've also drawn a graph of y equals one half and so you can see that there are infinitely many points where sine of theta does actually equal half.Trigonometric identities are very useful and learning the below formulae help in solving the problems better.There is an enormous number of fields where these identities of trigonometry and formula of trigonometry are used.I use Scientific Notebook or similar math software to graph the functions for me.You can use this Online Graphing Calculator to solve the following equations (or check your solutions) .When solving trigonometric equations, we find all the angles that make the equation true.If there is no interval given, use periodicity to show the infinite number of solutions.Sine is periodic with period 2pi so I can add any integer multiple of 2pi and get another solution, so my solutions will be of the form of theta equals pi over 6 plus 2n pi and that represents an even multiple of pi I could add any even multiple of pi or subtract any even multiple of pi and get a new solution or 5pi over 6 plus 2n pi.So both of these principles solutions yield infinitely many solutions.


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