# Solving Trigonometric Problems

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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.

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.

Now to get started let us start with noting the difference between Trigonometric identities and Trigonometric Ratios.

Learn more about Trigonometric Ratios here in detail.So the only solution for this part is x=(2pi)/3. Also, cos x=-1 gives x = pi. So the solutions for the equation are x=(2pi)/3or pi. A check of the graph of y=cos x/2-1-cos x confirms these results: Note 1: "Analytically" means use the methods and formulas from previous sections. Note 2: However, I always use a graph to check my analytical work. Solve the equation If the problem involved θ only, we would expect 2 solutions; one in the first quadrant and one in the second quadrant.But here our problem involves 2θ, so we have to double the domain (θ values) to account for all possible 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.Two ways to visualize the solutions are (1) the graph in the coordinate plane and (2) the unit circle.The unit circle is the more useful of the two in obtaining an answer. Let's start with a really simple example, sine of theta equals a half.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.

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